Belize: cave tubing for everyone but the little kiddos. I assume with that many ports of call you will be leaving the kids on the ship for one of them- cave tubing is really fun.
Grand Cayman: I suggest you definitely do an excursion- there isn't much to do just walking around. The kids will hate it. I did not go to Stingray City but met many people who did and they LOVED it.