Going on our first cruise in June - Carnival - myself, hubbie, and 6 (almost 7) year old son. The ship docks in Cozumel from 8:00 AM - 10:00 PM. My son really wants to do a dolphin encounter but we also want to do the beach. Is it too much to do a dolphin encounter in the morning and then do a beach experience in the afternoon? Thinking about it it doesn't seem to be but since it's our first cruise I'm not sure of the logistics. And for the beach, I've heard both good things about Santos as well as Nachi Cocum (not sure if I got that spelling right) - which would be better for a 6 year old that really wants to ride on a jet ski?
I have to totally agree with Snoozerman, you can plan to spend the day at Chankanaab Park. Its not far from the pier, plenty of taxi's to take you there and take you back. They have a huge beach, some great snorkeling, places to shop and eat, plus the dolphin swim is there.
You would have to find out the age restrictions, yes, there is some swimming involved, you actually are in the water with the dolphins. They pull you and do a nose push, so much fun. You do have to wear a life jacket no matter what age.