Not sure what itinerary you are taking but we loved the Inspiration. They have kids activities, camp carnival and one for the older kids as well. Should be lots of kids on board during spring break so your children should have lots of fun. My daughter will be 9 on our next cruise and she loves Camp Carnival. Very excited about being able to sign herself in and out on the next one. The kids do all kinds of activities on the ship such as scavenger hunts, plays, movie nights, play stations (video games), etc. Check out the capers each day for the activities. Also, be sure to either register them ahead of time on line or go to the registration the first night (I would recommend going the first night). You get a wealth of information this way.
There are lots of excursions you can do in Cayman and Cozumel. We did 7 mile beach on our own in Cayman ($4 / person each way for the taxi). This was much cheaper than the excursion ont he ship which was $29 / person. The beach is free and you can rent beach chairs as well as pay to do water sports as well. Cayman is really easy to get around on your own. Cayman is a tender port so you will have tenders taing you from the ship to the dock. Keep this in mind for the return time to the ship. Make sure you are at the tender prior to the time Carnival gives you to get back on the ship. I would recommend an our or so early.
For dining, we were in the dining room with Jeorge the Greek. He is absolutely awesome as a Maitre'd. If you can get his dining room I would recommend it. Also, Barry the piano man is in the piano bar every night. We had a blast with him. he makes sure evryone gets involved, is extremely nice and funny. Formal dining is also well worth going to. this is the night they have the lobster. Also, the chocolate melting cake is to die for. You have to try it if you like chocolate at all.
Feel free to keep asking questions. People on this board are very helpful and have a wealth of knowledge regarding Carnival. Happy cruising!!!