Carnival is probably the most family orientated main stream cruise line outside of Disney Cruises. Although Royal Caribbean Cruise lines is probably just as good as Carnival. Princess caters to an older crowd but they still offer a kids club and provide for families.
Splendor is a great ship and if you want to sail from California, probably your best bet for a relaxing family vacation as RCCL no longer sails from CA.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007