I was on that same cruise. Those ages make it tough! I would suggest mostly beach type activities. When it's hot, kids want to cool off in the water(as opposed to shopping and sightseeing). So, I would go to Rose Hall Beach in Jamaica, Chankanaab, Cozumel(possibly) for their walking trails and seeing the big lizards etc.. although there isn't a gradual walk-in beach there.
In Grand Cayman, the 6 year old could work well with the stingrays (3 year old may be petrified)depends on your kids and swimming abilities. My kids ranged from 15 to 20. If they were 3 to 6, it would have been an entirely different experience.