Consider Club Med (
www.clubmed.com , which has lots and lots of sites in the Caribbean where AA flies. Some clubs are geared specifically toward familiaes with kids: they've got activities for the kids all day, and everyone I've known who have brought their kids had a great time.
It's also a great time for the adults. While the kids are being supervised and having a ball, you can do as much or as little as you like.
Meal times are also easy (good, though hardly gourmet), because there's an enormous buffet and you can always find stuff you like.