Definitely let the kids drink.
Take 'em parasailing once with Tony. They'll have a ball. Spend at least one whole day fishing, snorkeling and having a beach BBQ. There is a wealth of guides who'll do that for you.
Take a drive up north and have lunch one day. Go to the Chicken Drop on Wednesday night and teach 'em to gamble. Spend a day or two in town and just hang out with the locals. Definitely go to Lamani (or Altun Ha). Take the cave tubing and Belize Zoo tour. Take your credit cards. Walk the beach. Repeatedly. Stay away from the 'gator feeding...something bad's bound to come of that sooner or later.
Seriously, there are lots of tours, fishing, snorkeling and such to do if you don't mind paying for them. Heck, enroll them in scuba classes and get them certified. That'll keep 'em out of trouble.