If I was taking a bunch of 6-15 year olds on a cruise, I wouldn't hesitate to choose RCI'S Voyager class ships, like Navigator of the Seas. They have a great kids program and have the extras, no additional charge, such as miniature golf, ice skating, roller blading, rock wall climbing and Adventure Ocean. Our grandkids had a blast, they didn't want to get off the ship when it was in port.
There is also a lot of activities for adults, and the ships are absolutely incredible with two Atriums and a Royal Promenade that has to be seen to be believed.