I'm supposing from your note that the four of you will be sharing a cabin. In that case, you'll need a "quad," which will have two single beds plus two beds that your steward will pull from the ceiling at night. Once down, they will look like bunk beds. During the day, they are once again pushed out of the way.
If you can swing it, see about a mini-suite. There is a pull-out sofa bed instead, and a lot more floor room. We had three in a standard balcony cabin on on of Sapphire Princess' sister ships, and it was a bit tight, although we managed.
Princess has fabulous kids' facilities. We traveled with friends who had a 9-year-old and he loved the kids program and couldn't wait to get there every evening. Kids are allowed in most of the ship's night clubs as long as they are with a parent. (Our son likes to dance, too.) Yet, the kids will have their own parties in their Club, as well.