A value resort would be a great place to start for financial reasons. Your family could book a Family Suite at All Star Music that will comfortably sleep 6 people with plenty of space to spread out and even 2 bathrooms. It's more affordable than the villas.
Your extended family could then book their own rooms at All Star Music. Maybe the grandparents in one room and the siblings spread out over 2 other rooms.
A Grand Villa will set you back $1300/night during value season compared to $246 a night for 3 rooms at the All Stars and an additional $179 a night for a family suite. Thats $1300 compared to $425.
Basically it could break down like this using max occupency:
3 rooms at Value resort (4 per room)
3 rooms at Moderate resort (4 per room)
3 rooms at Deluxe resort (4, maybe 5 per room)
3 1-bedroom villas at a DVC resort (4 max per room, 5 at AKL)
2 2-bedroom villas at a DVC resort (8 max per room, 9 at AKL)
1 Grand Villa at a DVC resort (12 max)
It's going to take some research into max occupency for each room category to determine all available options. With the DVC resorts (exception to Old Key West and Saratoga Springs) you'll have the option of booking a villa and a standard room at the DVC's sister/main resort.
Max Occupency for your party total:
2-bedroom villa (sleeps 8) and standard room/studio villa (sleeps 4, maybe 5)
two 1-bedroom villas (total of 8) and standard room/studio villa (sleeps 4, maybe 5)
The villas at Disney's Animal Kingdom Lodge will sleep an extra person (5 in 1-bedroom, 9 in 2-bedroom) due to the pull out chair in the living area.
We did a similar trips a couple of years ago and everyone agreed that we had a much more enjoyable time with our own space. A Disney trip is going to be overwhelming as is for a family of a five, nevermind factoring the needs and wants of 7 other people.
We didn't even factor in things like bathroom time, privacy, living space, etc on our first trip. We compromised our own expereinces for that of the "groups" in regards to touring the parks and trying to keep everyone happy. We learned our lesson the first trip and booked accordingly the next. We agreed to go to the same park on each day. We didn't force people to get up or wait for anyone either. We set one goal (lunch or dinner here, parade spot, etc) and agreed to all meet up at that point/time. We carried cell phones around and would always stay in touch with eachother. It gave us the freedom we needed so that some of us could do the thrill rides (Tower or Terror, Rockin' Roller Coaster, Star Tours, etc) while others were more laid back ( Great Movie Ride, Backlot Tour, Little Mermaid, etc). We did some attractions as a group, others seperate.
We'd always try and eat our table service meals together and catch a parade or show together. There were some days we hung out all afternoon others where we didn't see eachother until we got back to the resort. Everyone came and went at there own pace and at the end of the night we'd usually recooperate and talk/share pictures by the pool or in someones room.