The early show is before the late dinner (I think it starts at 6:00 or 6:30). On the 7 day, there is a family cabaret show in one of the clubs. On both ships there are family game shows like Mickey Mania and Walk the Plank held in Studio Sea usually. You can also enjoy the pools with much fewer people than are there during the afternoon, take a walk around Deck 4, play shuffle board, enjoy the adult lounges, etc. The kids program is usually in a movie around this time too.
Our family has always had late seating. We usually enjoyed the pools until about 5:30, got dressed for dinner, went to the main show, visited the cabaret show or the game show, and went to dinner. A couple of times our son was watching the movie, so he missed the show, but there was always plenty to do.