Susan:
Thanks so much for coming to the panel!
When our family of 19 came to WDW last year, we had the same philosophy. Our game plan was to either go to the same park each day and or eat one meal a day together. Outside of that, though, there was a lot of wiggle room to swap up the group (girl/guys; grandparents w/grandchildren; parents only; nuclear families only...).
As for touring, I would suggest Magic Kingdom and Disney Studios earlier in the week and Epcot later in the week when the crowds get larger. You may even want to plan two days for Epcot so you can keep an enjoyable pace. Since you're there for a week, a resort day and a Downtown Disney day can be planned, too.
Make sure that you register your party for a
Grand Gathering. It will allow you to make any dining reservations together earlier than the new 90-day advance window, and put you in touch with a Magical Gatherings planning specialist (407-934-7639) who will have up-to-date information on experiences your group might qualify for!
If you get a chance, take a peak at questions and answers from other large traveling parties
here. You never know when you might uncover a good nugget of advice!
Wishing you a magical vacation!
Whitney