There should be plenty for your childern to do. From what I have read on their web site about activities and comparing them to what e have experienced on Carnival, you'll probably never see your childern unless you catch them changing into swim wear or something.. Make sure you plan to meet up at certain times or bring walkied talkies to communicate.
As far as bad press, Cruise Fanatic's answer is probably some of it, the rest of the negative comments are coming from the group of die hard Norway fans who think NCL should stop pursuing profit (like EVERY OTHER corporation on the planet) ad sink money into a ship that is no longer profitable. (And now having said that, I will be attacked for my opinion, but so be it).
Go with an open mind and you will have a great time.
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