Your best bet would be Crystal Cruises since they offer a limited, seasonal youth program in the summer. The ships are also larger, thus offering more facilities that might interest youngsters. Another choice would be Cunard Line's QE2, which also offers a youth program. Once a summer, there also is a family cruise with special guest entertainment that kids and parents would enjoy (theater troupes, etc.). The QE2 is one of the few ships (other than Disney Cruise Line) that has a nursery for children under two years old which might be helpful to you.
The next level -- premium -- includes Holland America Line, Disney Cruise Line, and Celebrity Cruises. The first two have year round youth programs while Celebrity offers youth activities seasonally. They are not as exclusive as Crystal or Cunard, but they offer excellent service and good food (and in Celebrity's case, great food).
Good luck and keep me posted of your choice.
Luisa Frey Gaynor
Family Cruise Editor