@tink1970 laid out most of the important considerations. I can add a few more. We traveled as three related families and 9 people, so not as big as yours but we had some of the same issues.
1) Try to agree on a date and get it booked ASAP, but on the other hand don't rush so much that you make a bad call. Make sure the dates/locations/budget you agree on works for everyone. Remember, unless you are thinking Concierge (which is much more expensive) the deposit is refundable, so in a worst case you could book something soon and then re-book if you find something that works better for your family.
2) Look at the sizes of cabins, and the makeup of your family and decide how many cabins will work best. For the cruise we picked (late Summer) Veranda cabins were only 10% more than inside cabins. This allowed us to book a big 5 person "family cabin" and a connecting 4 person one. For a cruise, less rooms equals cheaper price, since the first two in a room cost more than the others. (Though this is less true for DCL than some other cruise lines.) Of course, only you know the personalities of your families to know how few rooms will work for you. We had my mother and my sister's family (her, her husband and two teen-aged daughters) in one room, and myself, my wife and my two teen-aged sons in the other room. We get along well with each other, so it worked well. Having connecting veranda's was great too, since that gave us two ways to get to each other's rooms (Most but not all Verandas can be opened up to the ones next to it if you ask). All the cabins are small, but there is a lot of storage space. The bigger rooms have a curtain between the two sleeping areas, which provide some flexibility.
3) Make sure to "link" your reservations. This will allow you all to sit together in the Main Dining Rooms, and it will allow you to see the excursions, spa treatments, Meet and Greets, etc. that the others in your party have booked and for which times. This makes planning easier. We did some things all together and some things in various sub-groups. It was great to "mix and match."
4) On the ship, plan to get the DCL app, and to have as many people as possible have either a smart phone or wi-fi capable device (like an old smart phone or iPod that still can get wi-fi) so that you can use the app's free chat feature. This was great for us. Once on board, it allowed us to see all of the menus and activities. It also let us chat back an forth with each other. This made meeting up with each other for various things much easier, and didn't make people feel like they "HAD" to do what everyone else was doing, since they could always meet back up as soon as they wanted. This put several people more at ease!
5) Another big difference between a cruise and most any other type of vacation is the kids clubs. DCL's are excellent. I don't know the ages of your children, and it is difficult to say ahead of time if your kids will want to be in the kids clubs, but they might. If you have several children in a similar age range, they might be even more inclined to go together. The clubs have both scheduled and unscheduled events. Some kids prefer the free times, others like specific activities. Either way, it may mean you have some adult time on your hands too, and the Adults only areas are also very nice.
There are many steps to the whole process. Book the cruise. Decide if you want to stay before and/or after your trip. (Highly recommended, especially before so you don't have trouble making the ship). Get airfare. Get hotels (if needed). Get transportation. Pick optional shore excursions. Reserve other things like Spa treatments, Meet and Greets, Alcohol tastings, etc.
It sounds like a lot, but it isn't so bad. You say you've been to WDW many times, so you are a veteran planner. Actually DCL takes much less planning than WDW. Having said that, you will probably want to have one lead planner, or maybe one lead planner per family. I was the main planner for our group, but I spent a lot of time talking to my wife, my sister, and my mother about what they and their familes wanted, and what they could expect. It was a long series of joint decisions. But I loved it. Planning that trip was as much of a family experience as the trip itself (almost!)
Have a great time!
Also, log in at midnight 75 days out to book! 
When it comes to check-in and booking online, try and work out a priority list, so the things you really want to book, you go there first and book. Then you can do the less important things. That way, at least you stand a slightly better chance of getting the things you want.
