Welcome Aboard, Greg!
A cruise is a perfect vacation for your large family! Since you have six family members, you will definitely need to book two staterooms. I would recommend connecting staterooms, which means there is a door connecting the rooms together.
One of the "hidden gems" on the Disney Dream and Disney Fantasy are the category 8E
Deluxe Oceanview Staterooms. There are only a handful of these on the ship, and they are positioned sideways with two large portholes, instead of the usual one porthole. I was lucky enough to be in one of these for a recent cruise on the Dream, and the room is humungous! One drawback is that each room only sleeps three people, so you could not put all four of your children in the same room to sleep. Also, the bathrooms in these rooms are not the split bath.
Two connecting
Deluxe Oceanview Stateroom with Verandahs is another wonderful option for your family. Not only is there a door inside the rooms, the wall between the verandahs can be opened up to make a larger area.
If you don't mind having an inside room, we have been on Deck 8 in two
Deluxe Inside Staterooms and been perfectly happy. My daughters LOVED the virtual portholes, and the rooms are nice and dark for sleeping anytime!
No matter which rooms you choose, you will be on a Disney Cruise ship, which is the best place EVER to be!
Happy Cruising, Tracy V.