Welcome LMR to Family Vacation Critic. Our forums are full of great advice and lots of posts regarding AI resorts. My family and are are taking our first AI ourselves this fall. I know Beaches has 1 bedroom suites, but the rates are a little pricey (for suites). However if that is not an issue check it out. There are 3 in Jamaica, I believe the Negril and Sandy Cay are in the Montego Bay area.
I haven't been to the Dominican, or Mexico yet but did a little research when planning our vacation and know there area ton out there. Family Vacation Critic also has wonderful resort reviews, including AI's, you might want to check that out. There are a lot of great tips going through the forum as well from families with similar questions.