If you are looking for your own little piece of paradise that also has great amenities for the kids, then book the cruise excursion called "Passion Island".
This private beach adventure is for cruise ship passengers only. I was told that the island holds 600 people but there were less than 150 on the day we were there.
Check with your cruise line for details. Through Royal Caribbean, the guests take a catamaran from the port (if weather allows it). So there is no age minimum for this excursion. However, Carnival guests are taken to the island on the thrilling Twister power boat. The Twister does have an age minimum. So check your cruise line for possible restrictions.
At the Cozumel port, we met up with our guide "Mr. Leo" who informs us that the seas are too choppy to take the Catamaran to Passion Island (as originally planned) - we would take a bus, then a short boat ride over to the island.
Passion Island is PURE paradise. It is deserted. It is for cruise ship guests only. It is OPEN DOMESTIC BAR and buffet included. The buffet has BBQ chicken, blackened mahi mahi, the best guacamole ever, tortilla chips, salad, rolls, fresh fruit and rice. For the kids, I couldn't have picked a better place. They had a water trampoline, but since the water was too rough, they brought out a couple of men to install a regular trampoline on the sand (no charge).
They have mini ATVs for the kids - FREE. The operator just "works for tips". They also have a playground and mini maze for the kids.
For the adults - they have some shopping there. Domestic bar. Covered restaurant. Hammocks everywhere. They had tables under the palm trees so you can eat on the beach. They have chairs in full sun. Chairs in shade. The merchants stayed in the shopping area so no one was walking around selling anything (except one guy with a box of Cuban cigars). We also saw some sea kayaks on the beach.
Restrooms and changing facilities are available. They were very clean (always important when you bring the kids)
So if you want to see what paradise truly feels like, book an excursion to Passion Island.