Rhapsody is a beautiful ship (we sailed on the Hawaii-Vancouver, BC cruise in 2000), especially the Solarium! She also 2 pools and 6 hot tubs, so you and your kids shouldn't run out of space in the water!
It's been my experience that the Vision-class ships have very good stabilization, and that even in choppy water, you probably won't feel much movement of the ship.
If you go to Grand Cayman, visit 7-Mile Beach if you can -- or Stingray City. Check out the Mayan Ruins in Mexico, and be careful in Jamaica.
AGREE - NO CONTEST - Even the best resort/hotel cannot come close to the attention/pampering one gets with a cruise. I like being steps away from my room - not carring items for a day's journey - even when taking shore excursions. Everything is not a $ sign but you are right - cruiser's get the better bargain. I refuse to stand in long airport lines or worse - held for hours on a tarmac. Hopefully, prices will stay in check so we can all continue to choose cruising.
We were on this ship from Galveston in NOV/DEC '01. We loved it we had the best time. We had an inside cabin on one of the upper decks but we did not care. The ship is really nice. The only thing I regret was getting a massage in the spa. It was too expensive and I did not notice any difference in the experience from the massage school here at home. This was our first cruise and I can not wait to go again. Let me know if you have any questions.