Not sure what your family enjoys doing, but if you like snorkeling, Belize and Costa Maya are fantastic snorkeling stops. I would not recommend staying on board, no matter what. At least go and explore the islands, if nothing else. RCCL offers "best of" type tours. Costa Maya, there isn't much sightseeing, it's a fishing village with a total population of about 100. However, you could rent a golf cart there and go into their town and visit the beach if you don't like snorkeling. There's also a swim up bar in the center of the terminal area, if you don't want to leave the port area. There's plenty of shopping.
Since we went snorkeling in Belize, I didn't go into town on one of the tenders either time I was there. The snorkeling trip picks you up at the ship. We booked it through the ship, both times.
If you're actually going to Cancun, I'd highly suggest visiting Tulum and/or Xel-ha. Normally, it's a 45-1 1/2 hour ride from Cozumel and then another 1/2 hour bus ride to Tulum or Xel-ha, but if you're actually porting there, you could easily spend a half day in each place, or a whole day in one.
Hope you have a marvelous cruise!