In Grand Caymen you need to tender to the island (you ride a smaller boat from the cruise ship to the island as it does not dock right at the port). If you booked your dolphin excursion through Disney directly, you don't need to worry about tickets, Disney will give you all the information and directions you need the night before. If you did not book with Disney, you will need to get your own tickets. They are (usually) given out in the Buena Vista Theater from 7:30-11:00; after that, no tickets are needed as there is less demand for the tender. Priority is given to people on Disney excursions. After that, they start giving out tickets to everyone else. It takes about half an hour to get to the island including loading and unloading as you have to wait for a full tender boat in order to leave. If you are not booked through Disney, you will need to take this into consideration when timing your excursion. I booked ours at 11:00, just to give us a bumper.
In Key West we are parasailing and then renting an electric car. In Grand Caymen we are going on an Island Tour (Hell, Governor's Mansion, Turtle Farm, Seven Mile Beach) and then splashing around at Margaritaville. In Cozumel we have the Mexican Tasting Workshop booked through Disney. I am not sure if your kids would enjoy these, but maybe you could use it as a springboard. No matter what, I am sure you will have a great time!
WE ARE SO CLOSE!