Kew Gardens is very very good for young kids there are lots of playgrounds and interactive kids things and a safe environment for them to run around in. Zoo is great (Also close to primrose hill to take in the view of the city afterwards) and the Aquarium, although I've not been, will be a winner for sure.
Army museum in Chelsea has a massive kids play area too but IME people just go for that and not the actual museum and it gets very crowded.
You could hire bikes and ride round Richmond Park, I take the kids there most weekends at the moment, great views of the city, deer roaming freely, loads of space to run around in but can get very busy on sunny weekends