Kris,
Your best bet would be either Royal Caribbean or Carnival. Both lines have excellent kids programs and both have the kids grouped by age. Carnival will take kids 2 and above and Royal will not take the kids until they are at least 3 years old for their programs.
As fas as Carnival being marked as a "party ship" this is not necessarily true, they have a very deversified age group. I think at one time before Carnival became as popular as they are and as big (remember they own Holland, Costa, and Princess lines) they were known more for the party crowd, and you will find more of that on the 3 and 4 day cruises, but on the longer cruises you will find more familys and all age groups. I escorted a group back in October on the 4 night Fantasy and we had 58 with us ranging from 2 years old to 70. Everyone had a great time and there was plenty for all to do.
If I can be of any assistance to you, please do not hesitate to contact me at :
cleopard@cruisesinc.com or you may call me at 1-866-750-3106 anytime from 8:00 am until 10:00 pm est.
~Carol~
Cruise Specialist
Cruises Inc.