I can't speak for Rhapsody, but for other RCCL ships I've been on it has been excellent. If you could work it out, I highly recommend the Voyager class ships, and particularly Navigator of the Seas. These are the best children's facilities I've seen, even better than Disney in my opinion. These ships have on average 1/3 children from RCCL news I've seen.
We traveled on Rhapsody this past June 2002 with our teenage children and with our grandchildren (6 and 11). Rhapsody is a beautiful ship that you will enjoy cruising on and the childrens programs were very good. (As good as any I've seen on any of our cruises). You and the children will enjoy all the entertainment, pool games and childrens facilities.
The first cruise that we took our children on was on the Rhapsody. They were six and eight at the time. They traveled on the Explorer of the Seas when they were eight and nine and loved the Johnny Rockets Diner. As my husband often said after the first family cruise the only problem we encountered was going home after the cruise and hearing "I'm bored" for the first few days since they had been entertained constantly for seven days on the cruise ship. I think RCI has the best children's programs, but we've never cruised with Disney before.