We did a few family vacations in the west when I was a kid.. Drove from Georgia out a couple times, and flew to Denver and rented a car once. Lots of stuff to see and do, but everything we did was FAAR apart. Yellowstone to Glacier to the Grand Tetons, the Badlands, Dinosaur, etc.. Riding in the car all day long kinda gets old. IMHO, finding a place to stay for a week would be nice. I think it'd get really old with that much family

The good thing about destinations on the east coast is that things are all pretty close together. Get out west and ya gotta drive. Or maybe that was just my family and a desire to see as much as we could during our time. I had visited over 40 states by the time I was like 13.
I really enjoyed Yellowstone and Glacier. Beautiful country out there. I still think it'd be fun to be a summer Park Ranger at one of those places..
What time of year are you guys gunna go? May wanna be a little further north during the summer, maybe further south during the winter... Grand Canyon vs. Grand Tetons