Keswick Museum is good fun - probably not for a 2 year old but for your older DC. Theres a xylophone made from slate they can play and a lovely stuffed badger as well as a huge 3 dimensional model of the Lake District.
Gentle walks:
Casterigg Stone Circle
St John in the Vale
circuit of Buttermere
If you go further west Muncaster castle has bird of prey demonstrations.
North, Carlisle Castle is fun.
Glava, the remains of a Roman fort me Ambleside.
If you want a bit of a sense of fell climbing, wandering around Loughrigg isn’t too steep. And a more ambitious but still easy walk from Grasmere to Easedale Tarn isn’t too hard.
Yhere are generally family friendly activities in Grizedale Forest. The climb isn’t particularly steep if you’re good walkers and you can look all the way down the length of Coniston Water and out to sea.
The ferry from Lakeside to Bowness on Windermere is fun, although crowded. There’s a steam train from Newbury Bridge to Lakeside so you can combine them. And in my experience, the enthusiasts who run the steam train love showing stuff to interested 5 year olds!
Of course nothing’s fun with 3 soaked children