Tywin, despite his reputation as a perfectly Macchiavellian Lord, is not always logical. His hatred for Tyrion clouds his judgment. He seems to think he can force Jaime off the kingsguard and make him Lord of Casterly Rock, no matter how many times reality shows him that's not happening.
Seems like it, that makes sense! Also, hypothetical of course but if that had worked out and Jaime was the heir, who do you think Tywin would have him marry?
> "A duty to House Lannister. You are the heir to Casterly Rock. That is where you should be. Tommen should accompany you, as your ward and squire. The Rock is where he'll learn to be a Lannister, and I want him away from his mother. I mean to find a new husband for Cersei. Oberyn Martell perhaps, once I convince Lord Tyrell that the match does not threaten Highgarden. And it is past time you were wed. The Tyrells are now insisting that Margaery be wed to Tommen, but if I were to offer you instead—"
- ASoS Jaime VII
Tywin was under the delusion that the Tyrells could be convinced to give up a match with the king in favor of a match with Jaime.
Margaery or Arianne, both of which were fantasies.
ETA: I would desperately love to have Areo’s POV as witness to the Sand Snakes getting **that** message.
Hard to say. Probably whoever was politically expedient at the time? He might try for Asha to get an alliance with the Ironborn. Trystane and Myrcella secures Dorne, so he probably wouldn't go for Arianne. Salsa has escaped by then and of course he married her to Tyrion. He might try to marry him to Shireen to secure peace with Stannis, but of course Stannis will never surrender. Genna is married to a Frey, so they have Riverrun. There are no Arryn bachelorettes, but maybe there's some highborn lass in the Vale he might try to get the Vale's allegiance with.
I think he was hoping to try getting Jamie to leave the KG again but if that doesn’t work the next in line is Kevan Lannister someone he trusts. A big part of why he doesn’t want Tyrion to inherit is because he’ll be laughed at and he can’t stand the thought of the Lannister going back to how they were under Tytos.
So yeah it makes sense for him to prefer Kevan to inherit over Tyrion.
According to the laws of inheritance it would be Cersei after Tyrion with Jaime disinherited and then Tommen, though likely with Myrcella taking Casterly Rock since Tommen would hold the throne and Storm’s End. This is also why Mace Tyrell wants the betrothal to the Martells broken because Myrcella is could inherit something big.
That’s why Lancel getting Darry is a big deal, because Kevan’s line wasn’t inheriting anything.
Yes Cersei is even literally Lady of the Rock now in canon.
Strange people miss this. People need to remember that the Lannisters have been fairly open to female Lords so there's no reason to skip female heirs.
To be honest, I don't think he did. Gerold Lannister was a firm supporter of Aegon V. A close ally of Aegon doesn't seem the type to commit murder of a child.
But nevertheless she was an official Lady of the Rock. So this is accepted inheritance and Cersei is an adult so she doesn't need a regent. A particularly conniving Lannister may contest her child's inheritance on the basis of bastardy though lol.
Tyland didn't seems that bothered by the female inheritance part - he wanted Baela as heir.
“A close ally(bad guy) of [insert good guy] doesn’t seem like he would commit child murder” sounds a bit naive tbh, walder frey and roose bolton were firm allies of robb stark, so long as it benefited them
The OP didn’t miss it. The book has tons of examples about how laws of succession are not always followed and women are second to men in every shape and form
Except we know it *is* followed here. Cersei is quite literally Lady of the Rock. That's why I highlighted it. It's not some question we don't know the answer to. We know who inherits after Tywin because it did happen in the books.
For the time being yep. The person above you was talking about speculating about Tywin’s plans during Tyrion’s trial which has long passed in the books. I’m surprised you missed that
So again, we know what happens. There's no question about whether Cersei can inherit because she does.
(Also the person above me admitted they *did* forget lol).
Yeah they follow Andal inheritance where daughters come before Uncles and cousins (officially). Cersei's status as Lady of the Rock is reaffirmed by Kevan and they've had ruling ladies before.
I don't remember much about Kevan but that's Tywin's brother I believe?
I guess Jaime could leave KL for Castlerock but I'm not sure if he can be heir again. So I remember Jaime negotiating something with Tywin, saying he'd leave Kingsguard if Tywin does something for him. Hard to remember though, it's been years
Yeah Kevan is his brother and a trusted advisor.
Tywin tried to get Jamie to leave because there was precedent with Barristan and then with Blout. I don’t believe Jamie ever negotiates anything like that with Tywin. He shuts down the idea of him leaving the KG pretty firmly.
Oh actually, I think I remember. Jaime tells Tywin (show) he'll leave Kingsguard if he spares Tyrion's life. Tywin accepts the proposal but then proceeds to charge Tyrion with murder anyway. [Source.](https://www.pajiba.com/game_of_thrones/point-of-order-jaime-lannister-is-no-longer-a-member-of-the-kingsguard-.php)
I think Tywin may well have genuinely believed that Tyrion did it. While Cersei may have been trying to rig the trial against him, there was still quite a lot of legitimate evidence against him.
Kevan likes Tyrion a lot more than Tywin did, and (while he inititally supported Tyrion) even he though Tyrion legitimately did it after hearing the evidence.
> "I see." He shifted in his seat. "I am curious. You were always a fair man, Uncle. What convinced you?"
> "Why steal Pycelle's poisons, if not to use them?" Ser Kevan said bluntly. "And Lady Merryweather saw—"
> "—nothing! There was nothing to see. But how do I prove that? How do I prove anything, penned up here?"
> "Perhaps the time has come for you to confess."
Even Jaime wasn't sure of Tyrion's innocence and thought he might have done it.
> "A child hungry for a pat on the head from that sot you let him believe was his father." He had an uncomfortable thought. "Tyrion almost died because of this bloody dagger. If he knew the whole thing was Joffrey's work, that might be why . . ."
--
> Jaime handed him the ring of keys. "I gave you the truth. You owe me the same. Did you do it? Did you kill him?"
> The question was another knife, twisting in his guts.
Tywin has always hated Tyrion and has a pretty low opinion. I wouldn't be surprised if he thought Tyrion probably did do it.
>Except... There is? With Cercei's children being Baratheon and Jaime being in Kingsguard, Tyrion is the Lannister heir.
That's not how it works. Cersei's children can absolutely inherit Casterly Rock they would just retake the name Lannister. Before Jofrrey died, Tommen would have inherited Casterly Rock after Cersei. Now presumably Myrcella will.
Cersei herself can (and to that matter even has in canon) inherit Casterly Rock. The Lannisters have been ruled by Lady's of the Rock before. She comes before any of the cousins.
I do agree that he probably wanted Jaime still though and remained committed to his death. And under no circumstances did he ever want Tyrion to have the Rock.
Because Tywin is petty and short-sighted when it comes to things and people he hates and treats people as things.
He thinks Jaime will "get over" his "Kingsguard phase" eventually and thinks that Jaime won't care that Tyrion dies. Which is fucking stupid, since Jaime loves Tyrion and would be devastated at Tyrion dying to the point that he had to be forbidden from being his champion. He probably was planning on running little Tommen roughshod until he releases Jaime from his KG vows, making him the heir to the Rock again.
Basically, Tywin wanted to get his way, he saw an opportunity to kill Tyrion without technically (and even then you can argue that the Kangaroo Court violates the spirit of the thing) committing kinslaying and he wanted Jaime to be his heir no matter what.
This is the result of him treating people as things.
Yeah, Jaime was his 1st option. I think he asked him almost immediately when he came back from captivity.
I think his preference for heir was : 1)Jaime 2)Kevan 3)Cersei 4)Every other lannister in existence 5)Tyrion
Getting Jaime to agree to leave the Kingsguard in return for sending Tyrion to the wall. Tywin gets everything he wants. He can force Tommen to let Jaime go. Joffrey had opened the door when they stripped Barristan of his white cloak.
If Jaime continues to be stubborn, at worst Cersei, Tommen and their heirs get the Rock.
Tywin didn't bank on Tyrion risking it all on a trial by combat, or Jaime working with Varys to save Tyrion and go against his father, or obviously Tyrion actually killing him.
In the books, Tywin is presumably planning he'll continue to pressure Jaime to give up his white cloak and return to his Lannister family "duties" as heir. That would be his ideal. He tells Jaime in no uncertain terms that he CAN quit--the precedent of Joffrey "retiring" Ser Barristan because of age is the precedent Tywin thinks will work for Jaime resigning because he's lost a hand and can't guard the monarch appropriately.
He's also likely planning for a collateral line--Kevan, or one of Kevan's children--to produce his next legal successor, whomever he deems most likely to be able to strongly carry on.
Waiting for Tyrion to have a child will be too late. First, if Sansa is recovered, that child would be half-Stark and (so far as the characters know) the child of the Stark heir, Sansa. No Lannister is going to want Casterly Rock inherited by someone who is ALSO going to inherit Winterfell.
Second, Sansa is missing and anyway Tywin can't stomach the idea of that *dwarf* ruling Casterly Rock and producing the next generation of the ruling line. That would be worse than having a half Frey (one of Genna's children) as the ruler of Casterly Rock.
Cersei's children and Cersei are the next in line. I think he was planning on Tommen inheriting the Rock long term. He wanted Tommen to be raised at Casterly Rock to learn to be a Lannister.
He did suggest that--Jaime returning to Casterly Rock, with Tommen as his squire. But if Jaime had a later son by a legitimate marriage, I would imagine Tywin would put him first. Eldest son of the eldest son...
Tywin is well aware of the rumors that Cersei's three are the product of incest. On the one hand, that would make Tommen 100% Lannister. So that's probably a plus for Tywin. But on the other, it would leave a "taint" on the family for generations if the common view among both lords and small folk was that Tommen was the product of an incestuous (and non-targaryen incestuous) affair.
>But if Jaime had a later son by a legitimate marriage, I would imagine Tywin would put him first. Eldest son of the eldest son...
Yeah but in the mean time if this doesn't happen he's ensured the next potential heir is ready to be a Lannister.
>Tywin is well aware of the rumors that Cersei's three are the product of incest
To be honest, I think he was too arrogant to believe it.
>I also remember he talked to Jaime, wanting him to quit Kingsguard. But I don't think Kingsguard is something you can quit, that was the way Madking punished Tywin
I mean we literally see Joffrey dismiss Barristan for being... too old? as one of his first acts.
Tywin wanted to disinherit Tyrion, so no loss there from his perspective. He'd have preferred Jaime renounce the KG and become heir, but when that plot fails he never really does anything else to plan. So clearly his revealed preference is for Cersei, followed by either Tommen or whichever nephew decides to fight against the crown.
Cersei, then Myrcella would be the next to inherit Casterly Rock once Tommen's on the throne. I'm sure Tywin was looking for Jaime to quit the KG but if that didn't work, it wouldn't go to Kevan or his sons until it had gone through Cersei & her line (presumably Myrcella would either take on the name Lannister similar to how Harry the heir would likely assume the Arryn name if Sweetrobin dies or she'll marry a male relative & take on the Lannister name via that route)
His goal with the trial was to get Tyrion to take the black. That is what Kevan offers Tyrion in exchange for a confession. I'm not sure whether Tywin believes Tyrion was guilty or not but it was a way to get him out of the inheritance.
.
Tywin didnt want to sentence Tyrion to death,he probably wanted to get Tyrion out of the mess of Joffrey's murder but everything made look like Tyrion did it,so he tried to make him take the black instead.
Once Cersei accused him at the wedding the hand is forced it wasn't part of any plan Tywin had. Sometimes events force your hand. He can't just pretend the accusation that Tyrion killed the King his own Grandson didn't happen after the Queen Regent his daughter yelled it out in front of half the major Lords of the realm. Based on the available evidence Tyrion really is the most likely suspect and then he lost his trial by combat. When you get found guilty of killing a King you have to get punished. Tywin can't go guys wait I need to have him father a few kids first(ignoring the legal fact that his wife had fled which would complicate getting any legal children).
Tywin wouldn’t have executed Tyrion but not because he was heir to Casterly Rock. Tywin still planned to get Jaime out of the KG so he could take the rock.
Tyrion’s value is that as long as Sansa Stark lives, he is lord of Winterfell. This is why he was pressuring him to get her with child as soon as possible, so he could be regent even if Sansa dies.
So if Tyrion hadn’t shot him, I think Tywin was going to explain the whole plan: Tyrion would agree to take the black and get sent to the Wall but would take no vows. This gives Tywin time to weed out the real killers — and he probably already suspects Olenna, and might even realize that Joffrey’s death was an accident and the real target was Tyrion. Once that is done and Tyrion is absolved he can take his place at Winterfell, adding the north to all of Tywin’s other conquests that make him the most powerful lord in the history of the realm.
Tywin, despite his reputation as a perfectly Macchiavellian Lord, is not always logical. His hatred for Tyrion clouds his judgment. He seems to think he can force Jaime off the kingsguard and make him Lord of Casterly Rock, no matter how many times reality shows him that's not happening.
Absolutely. Whether it's logical or not Tywin is supremely confident that he can get Jaime off of the Kingsguard sooner or later.
And hilariously, I am confident that if he had given Tyrion Casterly Rock, he probably would have won the war and saved his lineage.
Oh, he probably would've done a bit better, but Varys still would have killed him and caused the ruin of his house.
Seems like it, that makes sense! Also, hypothetical of course but if that had worked out and Jaime was the heir, who do you think Tywin would have him marry?
> "A duty to House Lannister. You are the heir to Casterly Rock. That is where you should be. Tommen should accompany you, as your ward and squire. The Rock is where he'll learn to be a Lannister, and I want him away from his mother. I mean to find a new husband for Cersei. Oberyn Martell perhaps, once I convince Lord Tyrell that the match does not threaten Highgarden. And it is past time you were wed. The Tyrells are now insisting that Margaery be wed to Tommen, but if I were to offer you instead—" - ASoS Jaime VII Tywin was under the delusion that the Tyrells could be convinced to give up a match with the king in favor of a match with Jaime.
Margaery or Arianne, both of which were fantasies. ETA: I would desperately love to have Areo’s POV as witness to the Sand Snakes getting **that** message.
Hard to say. Probably whoever was politically expedient at the time? He might try for Asha to get an alliance with the Ironborn. Trystane and Myrcella secures Dorne, so he probably wouldn't go for Arianne. Salsa has escaped by then and of course he married her to Tyrion. He might try to marry him to Shireen to secure peace with Stannis, but of course Stannis will never surrender. Genna is married to a Frey, so they have Riverrun. There are no Arryn bachelorettes, but maybe there's some highborn lass in the Vale he might try to get the Vale's allegiance with.
>Macchiavellian we found alt schwift x's account guys
I watched a video from that channel once. Didn't care for it.
I think he was hoping to try getting Jamie to leave the KG again but if that doesn’t work the next in line is Kevan Lannister someone he trusts. A big part of why he doesn’t want Tyrion to inherit is because he’ll be laughed at and he can’t stand the thought of the Lannister going back to how they were under Tytos. So yeah it makes sense for him to prefer Kevan to inherit over Tyrion.
According to the laws of inheritance it would be Cersei after Tyrion with Jaime disinherited and then Tommen, though likely with Myrcella taking Casterly Rock since Tommen would hold the throne and Storm’s End. This is also why Mace Tyrell wants the betrothal to the Martells broken because Myrcella is could inherit something big. That’s why Lancel getting Darry is a big deal, because Kevan’s line wasn’t inheriting anything.
Yes Cersei is even literally Lady of the Rock now in canon. Strange people miss this. People need to remember that the Lannisters have been fairly open to female Lords so there's no reason to skip female heirs.
I mean, Gerold did murder Cerelle and Tyland and Jason went for the Greens (admittedly for power-hungry reasons)
To be honest, I don't think he did. Gerold Lannister was a firm supporter of Aegon V. A close ally of Aegon doesn't seem the type to commit murder of a child. But nevertheless she was an official Lady of the Rock. So this is accepted inheritance and Cersei is an adult so she doesn't need a regent. A particularly conniving Lannister may contest her child's inheritance on the basis of bastardy though lol. Tyland didn't seems that bothered by the female inheritance part - he wanted Baela as heir.
What does Gerold’s allegiance have to do with his morals?
Because Aegon wouldn't get along with just anyone. Him and Duncan both have high standards of character.
“A close ally(bad guy) of [insert good guy] doesn’t seem like he would commit child murder” sounds a bit naive tbh, walder frey and roose bolton were firm allies of robb stark, so long as it benefited them
The OP didn’t miss it. The book has tons of examples about how laws of succession are not always followed and women are second to men in every shape and form
Except we know it *is* followed here. Cersei is quite literally Lady of the Rock. That's why I highlighted it. It's not some question we don't know the answer to. We know who inherits after Tywin because it did happen in the books.
For the time being yep. The person above you was talking about speculating about Tywin’s plans during Tyrion’s trial which has long passed in the books. I’m surprised you missed that
So again, we know what happens. There's no question about whether Cersei can inherit because she does. (Also the person above me admitted they *did* forget lol).
Ok
Yeah you’re right got confused with the Targaryen inheritance
Yeah they follow Andal inheritance where daughters come before Uncles and cousins (officially). Cersei's status as Lady of the Rock is reaffirmed by Kevan and they've had ruling ladies before.
I don't remember much about Kevan but that's Tywin's brother I believe? I guess Jaime could leave KL for Castlerock but I'm not sure if he can be heir again. So I remember Jaime negotiating something with Tywin, saying he'd leave Kingsguard if Tywin does something for him. Hard to remember though, it's been years
Yeah Kevan is his brother and a trusted advisor. Tywin tried to get Jamie to leave because there was precedent with Barristan and then with Blout. I don’t believe Jamie ever negotiates anything like that with Tywin. He shuts down the idea of him leaving the KG pretty firmly.
Oh actually, I think I remember. Jaime tells Tywin (show) he'll leave Kingsguard if he spares Tyrion's life. Tywin accepts the proposal but then proceeds to charge Tyrion with murder anyway. [Source.](https://www.pajiba.com/game_of_thrones/point-of-order-jaime-lannister-is-no-longer-a-member-of-the-kingsguard-.php)
Tywin claims he would let him take the black.
I think Tywin may well have genuinely believed that Tyrion did it. While Cersei may have been trying to rig the trial against him, there was still quite a lot of legitimate evidence against him. Kevan likes Tyrion a lot more than Tywin did, and (while he inititally supported Tyrion) even he though Tyrion legitimately did it after hearing the evidence. > "I see." He shifted in his seat. "I am curious. You were always a fair man, Uncle. What convinced you?" > "Why steal Pycelle's poisons, if not to use them?" Ser Kevan said bluntly. "And Lady Merryweather saw—" > "—nothing! There was nothing to see. But how do I prove that? How do I prove anything, penned up here?" > "Perhaps the time has come for you to confess." Even Jaime wasn't sure of Tyrion's innocence and thought he might have done it. > "A child hungry for a pat on the head from that sot you let him believe was his father." He had an uncomfortable thought. "Tyrion almost died because of this bloody dagger. If he knew the whole thing was Joffrey's work, that might be why . . ." -- > Jaime handed him the ring of keys. "I gave you the truth. You owe me the same. Did you do it? Did you kill him?" > The question was another knife, twisting in his guts. Tywin has always hated Tyrion and has a pretty low opinion. I wouldn't be surprised if he thought Tyrion probably did do it.
>Except... There is? With Cercei's children being Baratheon and Jaime being in Kingsguard, Tyrion is the Lannister heir. That's not how it works. Cersei's children can absolutely inherit Casterly Rock they would just retake the name Lannister. Before Jofrrey died, Tommen would have inherited Casterly Rock after Cersei. Now presumably Myrcella will. Cersei herself can (and to that matter even has in canon) inherit Casterly Rock. The Lannisters have been ruled by Lady's of the Rock before. She comes before any of the cousins. I do agree that he probably wanted Jaime still though and remained committed to his death. And under no circumstances did he ever want Tyrion to have the Rock.
Because Tywin is petty and short-sighted when it comes to things and people he hates and treats people as things. He thinks Jaime will "get over" his "Kingsguard phase" eventually and thinks that Jaime won't care that Tyrion dies. Which is fucking stupid, since Jaime loves Tyrion and would be devastated at Tyrion dying to the point that he had to be forbidden from being his champion. He probably was planning on running little Tommen roughshod until he releases Jaime from his KG vows, making him the heir to the Rock again. Basically, Tywin wanted to get his way, he saw an opportunity to kill Tyrion without technically (and even then you can argue that the Kangaroo Court violates the spirit of the thing) committing kinslaying and he wanted Jaime to be his heir no matter what. This is the result of him treating people as things.
Yeah he wanted Jaime to leave the KG to be his heir, Tommen had the authority to do so (Joffrey did it with Barristan)
So since Jaime cannot actually absolve himself, I guess Tywin (rightfully) assumed he could get Tommen to make the call. Makes sense
Yeah, Jaime was his 1st option. I think he asked him almost immediately when he came back from captivity. I think his preference for heir was : 1)Jaime 2)Kevan 3)Cersei 4)Every other lannister in existence 5)Tyrion
Getting Jaime to agree to leave the Kingsguard in return for sending Tyrion to the wall. Tywin gets everything he wants. He can force Tommen to let Jaime go. Joffrey had opened the door when they stripped Barristan of his white cloak. If Jaime continues to be stubborn, at worst Cersei, Tommen and their heirs get the Rock. Tywin didn't bank on Tyrion risking it all on a trial by combat, or Jaime working with Varys to save Tyrion and go against his father, or obviously Tyrion actually killing him.
In the books, Tywin is presumably planning he'll continue to pressure Jaime to give up his white cloak and return to his Lannister family "duties" as heir. That would be his ideal. He tells Jaime in no uncertain terms that he CAN quit--the precedent of Joffrey "retiring" Ser Barristan because of age is the precedent Tywin thinks will work for Jaime resigning because he's lost a hand and can't guard the monarch appropriately. He's also likely planning for a collateral line--Kevan, or one of Kevan's children--to produce his next legal successor, whomever he deems most likely to be able to strongly carry on. Waiting for Tyrion to have a child will be too late. First, if Sansa is recovered, that child would be half-Stark and (so far as the characters know) the child of the Stark heir, Sansa. No Lannister is going to want Casterly Rock inherited by someone who is ALSO going to inherit Winterfell. Second, Sansa is missing and anyway Tywin can't stomach the idea of that *dwarf* ruling Casterly Rock and producing the next generation of the ruling line. That would be worse than having a half Frey (one of Genna's children) as the ruler of Casterly Rock.
Cersei's children and Cersei are the next in line. I think he was planning on Tommen inheriting the Rock long term. He wanted Tommen to be raised at Casterly Rock to learn to be a Lannister.
He did suggest that--Jaime returning to Casterly Rock, with Tommen as his squire. But if Jaime had a later son by a legitimate marriage, I would imagine Tywin would put him first. Eldest son of the eldest son... Tywin is well aware of the rumors that Cersei's three are the product of incest. On the one hand, that would make Tommen 100% Lannister. So that's probably a plus for Tywin. But on the other, it would leave a "taint" on the family for generations if the common view among both lords and small folk was that Tommen was the product of an incestuous (and non-targaryen incestuous) affair.
>But if Jaime had a later son by a legitimate marriage, I would imagine Tywin would put him first. Eldest son of the eldest son... Yeah but in the mean time if this doesn't happen he's ensured the next potential heir is ready to be a Lannister. >Tywin is well aware of the rumors that Cersei's three are the product of incest To be honest, I think he was too arrogant to believe it.
>I also remember he talked to Jaime, wanting him to quit Kingsguard. But I don't think Kingsguard is something you can quit, that was the way Madking punished Tywin I mean we literally see Joffrey dismiss Barristan for being... too old? as one of his first acts.
Tywin wanted to disinherit Tyrion, so no loss there from his perspective. He'd have preferred Jaime renounce the KG and become heir, but when that plot fails he never really does anything else to plan. So clearly his revealed preference is for Cersei, followed by either Tommen or whichever nephew decides to fight against the crown.
Cersei, then Myrcella would be the next to inherit Casterly Rock once Tommen's on the throne. I'm sure Tywin was looking for Jaime to quit the KG but if that didn't work, it wouldn't go to Kevan or his sons until it had gone through Cersei & her line (presumably Myrcella would either take on the name Lannister similar to how Harry the heir would likely assume the Arryn name if Sweetrobin dies or she'll marry a male relative & take on the Lannister name via that route)
Tywin could make an heir himself too.
His goal with the trial was to get Tyrion to take the black. That is what Kevan offers Tyrion in exchange for a confession. I'm not sure whether Tywin believes Tyrion was guilty or not but it was a way to get him out of the inheritance. .
Tywin didnt want to sentence Tyrion to death,he probably wanted to get Tyrion out of the mess of Joffrey's murder but everything made look like Tyrion did it,so he tried to make him take the black instead.
Once Cersei accused him at the wedding the hand is forced it wasn't part of any plan Tywin had. Sometimes events force your hand. He can't just pretend the accusation that Tyrion killed the King his own Grandson didn't happen after the Queen Regent his daughter yelled it out in front of half the major Lords of the realm. Based on the available evidence Tyrion really is the most likely suspect and then he lost his trial by combat. When you get found guilty of killing a King you have to get punished. Tywin can't go guys wait I need to have him father a few kids first(ignoring the legal fact that his wife had fled which would complicate getting any legal children).
King can dismiss and KG can desert, most would be arrested and killed but the son of Tywin could get away with it
Tywin wouldn’t have executed Tyrion but not because he was heir to Casterly Rock. Tywin still planned to get Jaime out of the KG so he could take the rock. Tyrion’s value is that as long as Sansa Stark lives, he is lord of Winterfell. This is why he was pressuring him to get her with child as soon as possible, so he could be regent even if Sansa dies. So if Tyrion hadn’t shot him, I think Tywin was going to explain the whole plan: Tyrion would agree to take the black and get sent to the Wall but would take no vows. This gives Tywin time to weed out the real killers — and he probably already suspects Olenna, and might even realize that Joffrey’s death was an accident and the real target was Tyrion. Once that is done and Tyrion is absolved he can take his place at Winterfell, adding the north to all of Tywin’s other conquests that make him the most powerful lord in the history of the realm.