There is every chance I own enough pairs of Minnie ears to cater for all of us.
In all honesty the kids' favourite thing will probably be the pool, the moderate ones are better than the Values. (Art of Animation is a value and it has an amazing pool though - highly recommend.)
IMO the best moderate (and bizarrely the only one I haven't stayed in) is Port Orleans French Quarter. It's small so there's no bad building to stay in, has a good pool, a nice food court, a boat to Disney Springs and you can walk to Port Orleans Riverside which has a sit down restaurant and another food court giving you more options.
If your budget can stretch to it, I'd really recommend Gran Destino Tower at Coronado Springs. It's basically a deluxe resort for moderate prices, and you have all the amenities of Coronado Springs. It's a conference resort so loads of restaurant choice and the pool is a cracker.