A few of the WDW restaurants have tables that will seat up to about 10 people (the Whispering Canyon Cafe at the Wilderness Lodge is the one that immediately comes to mind). But I really can't think of any WDW restaurant that regular seating any larger than that. If you are dining with a large party and make normal advance dining reservations (ADRs) by calling 407-WDW-DINE, they will end up creating reservations at two (or more) tables to accommodate your group.
When you arrive at the restaurant podium, you can explain your situation to the host/hostess. Sometimes (but not always) they will be able to work with you, by pushing tables together to create a larger seating area for your party. I have done this a few times and had the most success at larger restaurants (for example, Chef Mickey's is huge, they have the ability to move things around a bit) and when dining at less busy times (if the restaurant is packed tight, they won't be able to tinker too much).
I do have an alternative for you, however. Have you looked into getting help from the
Disney Magical Gatherings Department? Magical Gatherings is a special group that helps make traveling parties of 8 people or more plan their vacation more smoothly. You can contact them at 407-934-7639. Even if you don't have them book your hotel reservations for you (it sounds like you already have your rooms reserved), you can ask them about Grand Gathering meals. These are meals that have special seating for large groups, as well as sometimes other surprises. I suggest you give them a call and perhaps you can arrange for some special experiences to keep your entire party together.