Hi and welcome. I am not cruising on those dates, but I have cruised on Imagination in the past. It's a great, well maintained ship.
In Jamaica, Dunns River Falls is a great spot where you can climb the falls. Your children will enjoy it very much. At least mine did. If you go, bring a waterproof camera and water shoes for the rocks.
I cannot stress to you enough to please stay with an organized group/excursion in Jamaica. Do not venture off on your own while there.
Grand Cayman - Stingray City is remarkable. You can swim with, feed, hold, pet, have photos with, the stingrays. Another great adventure to experience with your 2 children and, another excursion that our 2 children have fond, everlasting memories of.
Have a great cruise.