The only logical choice is the Polynesian. Full sized day bed for one of the boys, large rooms which will easily hold a pack-n-play for the youngest, easy access to the MK, zero entry pool, 24 hour food service at Captain Cooks, etc.
You might want to look into concierge service, in your case it could be a "break even deal". You'd get cold breakfast every morning, afternoon snacks, bottled water which you are encouraged to take to the parks, free strollers to borrow, a minifrdige in the room, evening desserts, a lounge to relax in.
Anne