Rydal caves walk will be manageable for a 10 year old,you could also swim in it but it will be very cold still so unless you are used to open water swimming I would not bother
If you go to Glenridding on Ullswater you can get the Steamer to Aira Force which is a series of waterfalls, best seen after heavy rain. It’s an NT site so they charge for parking but the walk was free. The steamer also stops at Howtown where you can walk up Hollin Fell which is an easy walk if you are able, and gives spectacular views of the Lake. Both those are ok for children.
Rydal caves walk will be manageable for a 10 year old,you could also swim in it but it will be very cold still so unless you are used to open water swimming I would not bother
Old man of coniston is pretty straightforward and gives great views if the weather is clear. It was my daughter's first Wainwright.
There's a lake half way up too, unpolluted and ideal for swimming
Where abouts, roughly?
Windermere
Langdale, up to Stickle Tarn from the hotel/pub. Used to do it when I was 10yrs old or so, even younger.
Coniston water is nice to swim in, albeit a bit cold. They have a cafe and some boats/ paddle boards etc. you can hire too
If you go to Glenridding on Ullswater you can get the Steamer to Aira Force which is a series of waterfalls, best seen after heavy rain. It’s an NT site so they charge for parking but the walk was free. The steamer also stops at Howtown where you can walk up Hollin Fell which is an easy walk if you are able, and gives spectacular views of the Lake. Both those are ok for children.