On our trip this past February, we rented a room at the Atlantis so that we could use the pools. We have a five year old DD and twin boys who were 15 months at the time of the cruise. At the Atlantis you can take them inside through the aquarium, and there is a ton to see outside as well. There is beach area inside the resort with water from the ocean, but it is shallow with no waves. There is also a huge kids pool behind the big Myan temple slide that we discovered about half-way through the day. Once the boys found that, we were there for the duration.
The room also gave them a place to nap for a bit.
If that all sounds like too much, I would stay on the ship. But keep in mind if your twins are not potty trained, then they have to stay in the one ear of the Mickey Pool that has little fountains (cannot use the pools), which might get old for the entire day.
Have a great cruise and don't hesitate to use Flounders to watch the kids. They are fantastic and will allow you to have a little alone time, which is nice.