First of all, you are going to love the Conquest. She is a top notch ship.
Our children are older than yours, however they have a huge arcade and I saw children of all ages (including myself,
) with lots of variety to choose from for all ages.
On the aft of the boat is a more shallow pool, actually used by Camp Carnival, and other activities on the back deck for younger children.
My brothers children loved Camp Carnival, and when he came to retrieve them after each stay there, his kids left kicking and screaming. they had so much fun, they didn't want to leave.
I am assuming that the Conquest is still on a Western Tour (Jamaca, Grand Caymen, and Cozemel).
Honestly in Jamaca, you might stick to the beach or even go to Jimmy Buffets
Margarita ville. I sits right on the water and had those big water trampolines for the kids (under supervision of course). You have a beautiful view and we even had lunch. We also visted the town and I would not reccommend that. We were constanly hassled and our teenagers were offered drugs. The taxi drivers even fight over your business. However at Jimmy's, the staff took us out the back way to a nice old man's taxi. I felt sorry for him because if this is how he make his living, he is working with a pack of wolves. We were glad to give him our business. Atfer 45 minutes, we had , had enough in town and left to Jimmy's. They have a nice row of shops at the pier. Others may can give you some other places to choose from. I hear Dune River was nice, but is a two hour trip to and fro.
In Grand Cayan, the town itself is wonderful and right their at the pier. The people are exceptionally friendly. They also have a beautiful beach and a place where you can swim with stingrays.
In Cozemel, we went to Dolphin Discovery, which also has a beautiful beach with snorkeling, a musem type tour and replicas of ancient Myan ruins that you can walk through. It was very clean and I saw lots of families there. You can see the ship from the beach. We did the dolphin swim and though it was very pricey, we loved it. The animals are so gentle. We spent 6 to 7 hours there, had time to go back to the ship for a meal, clean up and then go to twon for a few hours of shopping. This was my third trip to Cozemel. They now have a big villiage right there at the pier, but prices are still better in town. The folks down there like to "negotiate". You don't find that at the pier.
Another thing you might consider. The ship excursions in my opinion are over priced. We did everything on our own and never had a problem. From the pier in Mx, we hired a taxi to the Dolphin park for $11.00 for the car load. The ship had advertised "sold out "on the dolphin swim, however we walked up and paid right at the park, saving 1/3 the price and had our turn after only a 30 minute wait. We really saved in my opinion. My brother had gone before us and did the same thing. he did his own excursion, saved money and had no problems. We just used cautioned common sense.
I think no matter what, you will have a great time!