Hi Palioye, welcome to Cruise-Reviews! You've selected a great ship and a great itinerary. In Cozumel I highly recommend Chankanaab Park, especially for the family. There is all sorts of water activities, snorkeling, kayakying, great beach, swim with the dolphins, and a zoo. There is a restaurant with bar service. The waiters never let you go thirsty, including water. You can easily do this on your own. Grab a cab and head on down. The entrance fee has gone up, I believe it is $19/per adult, children are less expensive, but it is very clean and you'll have plenty to keep the children entertained.
Ocho Rios, I do recommend you do a tour through the ship. Jamaica is a beautiful, but poor island. With 3 children, please stay with a group. Dunn's River Falls is the huge attraction there. You would probably have to carry the 2 year old, though, as you are actually climbing a fall on the rocks. There are guides, but I doubt the year old could do it on its own.
Grand Cayman, the big attraction is Stingray City. However, 7 mile beach is a beatiful beach and can easily be done on its own. You can grab a cab (which is really more like a bus) and they'll take you down there. I believe it was $4.50/each. You don't have to worry about getting back, either, there is plenty of transportation going and coming to 7 mile.
Great Stirrup Cay is NCL's private island, so no excursion is necessary. It's a great beach day. They do have water toys, a bar-b-que, and plenty of things to keep the children happy.
You'll have a marvelous time, I'm sure, and I'll bet you'll be hooked on cruising when you get back. Be sure to have the sticky buns in the morning. They're in the main buffet area and they're wonderful!