Have your travel agent check how many kids are onboard. I suspect there will be a bunch, even though it's the week before the Christmas cruise. If there are, there will be plenty for kids to do and you won't even see that much of them.
I would bring something for them to do on the flights, while awaiting transfers, embarkation day, and at other "in between" times. When the ship is underway, they will find plenty to do in the youth and teen programs. There's also a card and game room on the Promenade Deck where they can borrow popular board games, playing cards, etc., to play there or elsewhere aboard ship.
I noticed a surprising number of school-age children aboard MV Sea Princess during the first week of November, and soon learned that many California school districts adopted staggered school schedules in which 1/4 of the students and teachers are always on vacation (after which they return to a different classroom) rather than building more schools to accommodate the number of students. The "Mexican Riviera" itineraries apparently are drawing a lot of Californians, so you probably will find more children than you might normally expect at the time of your cruise.
MV Sea Princess is a magnificent ship. Bon voyage!