You don't say if you're on the Wonder or the Magic. Both ships have family activities in Studio Seas (usually) between the 1st and 2nd seating. These are typically game type shows such as Walk the Plank, or Mickey Mania. Three or four pairs of people are chosen to answer questions for prizes. They will also have family karaoke, and family dance parties there.
On the 7 day cruises, there are family cabaret shows between the dinner seatings. Those were my family's favorite thing to do. We really missed it on the 4 day Wonder trip. Basically, the entertainers will do a short show that they gear for families. We had a ventriloquist, a juggler, a singer who would take requests, etc. Lots and lots of fun.
After you look at the navigators, if you have specific questions about a particular activity, feel free to ask. It's a good bet that someone on this board has done it.