If you have never been to Jamaica before, I highly recommend the tour which combines Prospect Plantation with the visit to Dunn's River Falls. Wear your swimsuits under your regular clothes and bring along your towel and a pair of Surfwalkers (nylon mesh footwear with thick rubber soles) to climb the falls. You can leave your clothes and valuables in the tour van, where the driver will guard them, while you do the climb.
At Grand Cayman, all of the excursions seem to be winners but three options stand out.
>> Stingray City constantly gets rave reviews from those who go.
>> The "Sea and See" tour hits all the really unique destinations.
>> Seven Mile Beach (you can go on your own) is one of the best in the world.
Additionally, you will find real quality merchandise in the shopping district of George Town, which is right by the tender pier. BTW, the rum cakes (from a stand in the shopping district) are fantastic -- the coconut flavor is my favorite.
On Cozumel, I disagree with Nanatravel's comments regarding the local Mayan ruins at San Gervasio. Although not as extensive as Tulum, they are far more significant because the island of Cosumel is a holy place in the Mayan religion. Additionally, the folkloric show in the city of San Miguel de Cozumel (available on a combined tour that also visits the San Gervasio ruins), is one of the best that I have ever seen.
The tour to Tulum is outstanding, and the ruins there are quite extensive. Nonetheless, it is a relatively long journey (a ferry ride across the channel to Playa del Carmen followed by over an hour on the bus to Tulum -- and, of course, the reverse on the return trip) so it will be a long day. I'll leave it to your judgement as to how your youngsters will handle such an excursion. If you do decide to go to Tulum, be sure to bring one large bottle of water per person as the area tends to be very hot (typical daytime temperatures are in the 90's in the middle of winter).
I have also heard from several sources that the new park at Ex Carat is outstanding, but it also entails a full day outing with the ferry+bus tranportation arrangements.
The Western Caribbean route is one of my all-time favorites. Do have a great cruise!