Hi Katie! That sounds like a great trip! Having just helped a family plan for a Walt Disney World trip for 19 people, I highly recommend that you go to an Authorized Disney Vacation Planner. These planners are highly trained to plan trips for any size group and any size budget. I helped my friend with the basics, but then sent them to a planner.
It doesn't cost you anything to use one, and they can plan everything about your trip: airlines, resorts, dining, etc. You can Google "authorized disney vacation planner" to find one near you. You could gather representatives from all four families and then sit down with the planner, and they can put the trip together for you in a neat little package.
My own personal advice-- I would plan one time per day when everyone gets together. We usually do a sit-down meal together. Some fun ones are the
Hoop Dee Doo Musical Revue dinner show and
'Ohana restaurant at the Polynesian. Another fun thing for large groups is the
Pirates and Pals Fireworks Voyage. It is just too hard for families to try and stay together all the time and it ends up being not fun for anyone. When we travel with my cousins, who have girls, my boys are not at all interested in the things they want to do, so we just pick a time to meet each day and then go our own merry ways!
I hope this helps, and I hope to help you plan for the Wine and Dine half marathon next year. It is my favorite runDisney race!!