Your kids will love the Adventure of the Seas. My nine year old daughter has been on 12 cruises yet the AOS last year was her favorite -- fun youth counselors, great rock climbing wall, excellent ice show, etc.
As for shore excursions, you may want to read the article I wrote on this site called "Back to the Beach" which lists family friendly beaches in the Caribbean.
Feel free to ask any add'l questions.
Luisa Frey Gaynor