I'm not sure about the rates, cut I definately think that some fantastic ships for families would be Voyager/Explorer/Adventures of the Seas. There is just so much to do on these ships, virtually something for everyone. We just loved Explorer this last April and would recommend these ships to anywone. I think if you check around you can find some good bargains:
WE HAVE TAKEN OUR 2 CHILDREN THE LAST 2 YEARS THEY ARE 9 AND 11. WE WENT ON THE CARNIVAL DESTINY AND THE TRUIMPH. THEY LOVED THE KIDS PROGRAM AND THE WATER SLIDE. WE ARE GOING IN JAN. ON THE EXPLORER. THEY ARE LOOKING FORWARD TO ALL THE FUN THINGS TO DO.