Sounds like the cruise I took in February 2008 on the Carnival Cruise lines Valor Grand Cayman, Belize, Roatan and Cozumel. I dove in all 4 stops.
Grand Cayman was great diving
Belize was excellent diving It was about 40 minutes to an hour to get to the dive site by fast running boat. Recommend diving and forget the snorkeling.
Roatan was IMHO better than Belize
Cozumel - drift diving and a lot of sun rates right up there with Roatan. The currents I encountered were moving but with effort you could swim back to something you whizzed by. Others found the currents rather strong on their visit and swimming back to see something was not an option.
You can book through the cruise lines on all the ports and there are advantages to doing so. But you can save money by booking yourself. Cozumel for example is $60.00 for 2 tank dives if you book yourself.
I took my own gear with me. In June of 2008 I heard a first hand account of an event that occurred in Grand Cayman at a dive shop in a cement building. Readers Digest Version - Hurricane, clogged toilet, SCUBA tank and 2nd Stage used to unclogged the toilet and was returned to rental stock with out even being rinsed off. Really made me glad I had brought my own gear as the dive shop was the same one the cruise line used. I also observed that at every stop the rental gear the others used was rather well used and the water had lots of champaign bubbles from the gear.