We were in Cozumel last year when we took our first cruise on the Carnival Conquest and will be heading there again this year June 27. Both our kids (daughter 13, son 15) were scuba certified before we went so we did an amazing 2-tank dive on Santa Rosa reef. Cozumel is a great place to dive due to the clarity of the water but it's also a fantastic place to snorkel which is a lot less expensive.
Since this is your first cruise I'll throw out the usual PSA - if you book shore excursions on your own, you must make sure you are back on the boat prior to the designated disembarkation time. The boat will not wait for you. If you book your shore excursion through the cruise line, you may get the feeling like you're being herded or not like the time constraints but if your taxi gets a flat tire or something else goes awry, chances are the boat may give you that extra 10 minutes or will make accomodations. It happened to us in Jamaica and we literally got straight off the taxi, walked up the ramp and had the port doors close right on our butts. LOL!
When you get off the boat in Cozumel, you will walk right into a cluster of shops. Save that for when you head back to the ship. Believe me, they will stay open as long as the boat is at the dock.
Look through the shore excursion offerings the cruise line offers and if one doesn't fit then plan your own. The people on Cozumel are hard-working and friendly. Yes, there are those who will take advantage so beware.
One place to visit if you want to snorkel is Chankanaab National Park. It has nature trails, snorkeling, and places for relaxation. There is even an underwater cave that has spring water coming out of it which is really cool. You can usually find some 3-4' tarpin and schools of bait fish swimming around it and when the fresh water mixes with the sea water it is pretty neat. Since it is a national park, you will be prohibited from taking any seashells from here. If you must have a seashell from Cozumel, wait and purchase a cleaned one from the souvenier shops. You really don't want to end up with a shell in your cabin that has an 'occupant' of its own. When they die, and they will, they will begin to stink.
If you decide to snorkel, be careful of the amount of jewelry or metallic/shimmery clothing. Some fish, like baraccuda, are attracted to it because it resembles the shiny bait fish they like to eat. Not trying to panic you, just prepare you. The actual number of attacks is extremely low (perhaps nonexistent); but that is advice I've lived with and have been in the water with some pretty big barracuda and watched them snap a fish in half. You wouldn't wear a red sweater in a bull ring - the same principle applies here. Here's a link I found for the park:
http://www.tripadvisor.com/Attraction_Review-g150809-d185...
We always book the late dinner because we don't like to rush back to the boat, jump straight in the shower and head to dinner. We like to 'mosey' back to the boat, go to the balcony and watch the coast as we leave the habor, take photos, people watch and recap the days events.
Be sure to read over the Carnival Caper or whatever they call the daily newsletter on board. It will be full of events going on during the day. There were clubs for our kids but they actually had more fun just hanging out on the ship, playing volleyball, basketball, shuffleboard and water slide. I think they got in the pool once.
Carnival has some forums on its website where people can ask questions so check there also. You can be as busy or as boring as you like on the boat. There will probably be a shopping consultant of sorts on board so keep an eye out for deals they are sponsoring. There were shops at the ports of call who would give you a free charm for a bracelet if you had the promotional card and one of the shops actually gave the chain to go with it. If you're big soda drinkers, you can bring a certain amount with you when you board. They provide tea, water, lemonade, coffee, and cocoa free of charge. Or, you can buy a soda card for unlimited sodas but I thought it was kinda pricey. Next time we cruise, I'm bringing an insulated mug to put tea or icewater in for when we're chillin' in the recliners on deck. Their cups from the dining room are kinda small and the ice melts too fast.
I hope you and your kids have a fantastic trip! Safe and happy travels!