How about the ventura? A ship purpose built for the job it seems? Many Royal Caribbean ships are also like theme parks at sea. It may just be a case of finding a ship with an itinerary that will interest your children that also departs within the school holidays! Most cruise itineraries are not surprisingly aimed at adults rather than children. I'm sure that you can work out the best and worst destinations for kids yourselves? Happy cruising.
Disney have several cruise ships so you could do 7 days at Disneyworld and then join their cruise ship for 3;4;5 or 7 days sailing out of Port Lauderdale in Florida.
Try Royal Caribbean, they cater very well for children and have a variety of destinations and prices to suit all.