Hi there, I've been to each of these shops with my boys who are now 5 and almost 4. I'm not sure what to advise on Key West, we've only looked around the town there and gone on the basic tram tour. I don't really recommend doing that. I know there is a beach not far from the ship. If we were going there again, we'd do that.
Cozumel, doing it all over we'd go to Chakanaab. We've done a snorkeling tour from what we thought was a beach there. The beach was all rock/coral. It was NOT good for our son who was then 17mos. The other time we were there, we got a "beach break" pass to some hotel's beach. Our day in Cozumel got rained out, so no beach.
As for Grand Cayman, we took the tour that went to the Turtle Farm, Hell, and a picture stop at 7 mile beach. It was ok, but we thought it was a waste. Seven mile beach is GORGEOUS. You won't regret it if you just do that. That tour doesn't allow any time for swimming. It also spends forever "talking" about the turtles, and too little time petting the turtles. There is a mall right off the ship. Go in there to its turtle tank. At least she can spend the time she wants to with the turtles instead of being dragged back to the bus. Seeing Hell was ok, and a cute picture stop. If we had it to do all over again, I'd take a taxi to 7 mile, and on the way home, have the taxi stop at Hell for pictures, and head back to the ship.
I'm the family cruise editor here and I have a few add'l suggestions:
* Key West: Walk around on your own. Mel Fischer's museum has great treasures found from sunken ships. There is also a small aquarium in Key West near Mallory Square. Make sure you bring your stroller and get a map because there's a great spot called Nancy Forrester's Secret Garden (it is a bit hard to find unless you have a map). YOur daughter will love the exotic parrots and macaws there. When we visited, Nancy herself took them out and they performed tricks for us! My 7 year old daughter thought it was great!
* Grand Cayman: Yes, definitely take a cab to Seven Mile Beach. The cabbies know which beach clubs accept day visitors and there's a small charge to use the beach. Nice beach, calm waters, and very lovely!
* Cozumel: When my daughter was about five, we took her to a folkloric dance show which she enjoyed. However, since yours is younger, perhaps a beach transfer from the cruise line would be best.
I hope this helps!
Luisa Frey Gaynor
We just did this itineray with our 2 year old. Now, our daughter has been swimming (i.e., in the pool) since 6 weeks old so is very acclimated to the water. She and her mom did the stingray/snorkel excursion (with Captain Marvin's not a ship excursion) - it was a family group of 8 (I took mother-in-law on taxi tour - just OK - she got the rum cakes she wanted - I would have preferred the snorkeling). What we did was have her swim with some goggles on before we left (and also with a life jacket) so she was kind of ready for the goggles and life jacket at the snorkeling/stingray sights. She loved it but she has always liked the water (her mom is a swimming teacher). (Wish I'd know about the mall with the turtles in the tank - the turtle farm isn't much to see - other than the fact that youjust don't see that many turtles in one place). The beach is also free and there are designated access points - but I think a "beach pass" from a hotel would be nicer.
Key West - Luisa's ideas are very good - plus if they still do the Mallory Square sunset "party" when you're there, there's lots of entertainment there - including - on the Hilton property right by where Rhapsody docks (I'm guessing you're on Rhapsody as I think it is the only ship that docks at 3) - "Dominique the Cat Man" - I kid you not, trained house cats that jump through hoops and the like. Dominique is a trip (he's been on Leno for what that's worth) and unless your daughter hates cats she'll be entertained - lus in the square there are jugglers, tight-rope walkers, etc. We did the trolley tour and it wasn't bad - the adults enjoyed it but toddler was obviously bored - but everything can't revolve around her!
Cozumel - we went to Chakanaab. This was a good choice. In addition to snorkeling there is a small children's sand beach with sand for building sand castles and a protected swimming area. Plus there's the gardens, etc. A short taxi ride (and I think the 3 year old is free). We didn't eat there (grandmother was getting tired) - so back to the ship for her and toddler nap in stroller while we shopped. I hated Carlos and Charlies - too loud, too vulgar, but then 20 years ago, I might not have felt the same way. Did find a nice mall not far from there with lots of sourvenir shops and a guy selling two beers and a shot of tequila for $4 - so the husbands sat and drank beer (rocked toddler), the wives and teenagers "bargained" for souvenirs (and the wives added our tequila to their margarita). It was shady and quiet. I don't know the direction, but if you face Carlos and Charlies and then go left you'll find it. Rhapsody docked right across from Carlos and Charlies that day - on the other hand, if you dock elsewhere, there is a great market right across the street from where you come off the street.