DD breaks up on the 16th for half term.
Lau - check out Lowther castle, because you're quite near there. My girls love it! Best for a dry day because it's all outside, but they have a huge wooden castle play area, lots of logs and tree stumps they've made into a balancing course and rope swings. You can take a picnic or there's a tea room.
Ullswater is nice. We took a steamer across the Lake then walked up to Aira Force waterfall, which isn't too far.
I've never been to Rheged, but there's indoor stuff there.
At Keswick there's the swimming pool, with waves and slides. There's also a small indoor play area that also has indoor caving and climbing walls. And of course the Pencil Museum!
We like having a walk around Buttermere (it's a flat walk) then stopping off at the cafe there for one of their ice creams.
Whinlatter is great for kids.
There's good play parks at Keswick and Ambleside.
We liked the grounds at Mirehouse, there's different play stuff for the kids.
There's an aquarium at Maryport.
We like Brockhole on Windermere, although it's been summer when we've visited, so you'd have to check what's on in winter. We've done kayaking, golf, tree top nets, playground there before.
I'm trying to think of more indoor stuff, but mostly we take our waterproofs and go out for walks anyway!