Michele, welcome aboard!
I'm so glad you asked about Port Adventures in Grand Cayman, because I went on one of my favorite adventures there. My daughter and I went out to Stingray City which is a shallow area of water way out in the ocean where many stingrays gather. Sounds a bit scary? It's not. These creatures are gentle and really unique to swim amongst. I would highly recommend doing this with your kids. Disney Cruise Line offers a few different Port Adventures that go to Stingray City. I'd recommend the
Stingray City Snorkel Tour for your family. Don't worry if some of the kids haven't snorkeled before. The don't even need to put their masks or snorkels on to see the stingrays. The water is so clear, they'll have no problem enjoying this even if they keep their heads above water. The water is shallow, so they can probably stand at most points, or float with their life vests right around you, which is what my daughter did a few years back when we went. I think the kids would really enjoy interacting with and learning about the stingrays.
If your family wants to see more of the island as well as Stingray City, check out the other Port Adventures that stop at Stingray City. Some of them include additional stops, such as the Turtle Farm.
In Cozumel, your family might enjoy checking out one of the Port Adventures to a local beach, or possibly to the Mayan Ruins to learn about the history of the people in that area.
On the ship, you'll notice that it is breezier on days at sea, and cooler in the evenings. Check the weather online for the ports of call about a week before you go, then throw an extra sweater or light jacket in your suitcases for cooler nights and breezy sea days and you'll be all set.
Have a wonderful cruise, Michele!