Not sure I would take young ones 'deep' sea fishing, if they get bored or seasick that could become a $$$ downer.
Kool Runnings is the water amusement park. Otherwise I'm sure your kids will be thrilled with the beach and sea, and doesn't Beaches Resort have an extensive program of offerings for the kids? You will NOT run short of things for the kids to do, let them enjoy the resort amenities while you and your wife enjoy 'your' time.
I recommend people enjoy a day 'off' at their resort/on the beach between excursions days. Too much running around/logistics management and you might lose sight of vacation.