As others have mentioned, deffo Fell Foot Park. There is a nice playground (only small though) and you can buy duck food to feed the ducks on the lake. You can take a very short ferry ride from Fell Foot over to the Aquarium. It's a lovely place to walk round or take a picnic and a ball.
Lakeside and Haverthwaite railway is good if you have a train buff (my boys love it!). This also goes to the aquarium.
The aquarium is good but not much for your money I don't think.
You can take an open top bus sightseeing ride through Bowness.
If it's a wet day, there's a wacky warehouse at Barrow and there's a soft play area in 'The Piano Bar' (I think it's called that!) in Ambleside.
Brockhole is fabbo - loads to do there - outside playground, indoor interactive exhibitions and you can take a ferry ride from there too.
You should be fine on the ferry - you can sit inside if you are worried about safety.
A bit of a drive up north but there is a potteries place where you can paint plates and bowls and there is a playground there and animals to see too. It's called Wetheriggs in Penrith. Another good one if it's wet.
I've not done Muncaster Castle or the Dalton Zoo but both have been recommended to me.