We did a similar situation for our kids first Disney trip (DS 8, DS 7, DD 5)...my parents came for whole week and my MIL came for last part of week. We did two rooms at WL (1queen, 2 bunks). The 3 kids moved around between rooms and everyone got a "real" bed. I planned a dinner out for my parents (anniversary celebration) at California Grill. I also planned a night out for my husband and his Mom. It was great to swap kids around and get a break now and then. Plus, DD couldn't do RNR coaster since she didn't meet ht requirement, but she met Minnie with my parents while we rode coaster with the boys. Everyone had a magical moment! We planned meals and parks...but this was before FP+. There was flexibility. My parents took time to tour alone.
I would offer the invite. I would suggest two rooms for separation. Plus, it would be easier to drop a reservation if someone can't make the trip. And...don't be afraid to ask for some family time alone if they come the whole week...allow them time alone. You could get them a spa package or golf tee time or a dinner/lunch reservation or something that interests them to guarantee time alone as a family, but w/out having them feel left out!
It is Disney...It is your first trip...It will be magical! Don't overthink it too much or you'll stress out....I am sure your parents just want to experience the reactions by your kids! Mine are dying for my brother and SIL to take their kids (they keep putting it off as other vacation time commitments come up - family weddings for my SIL's family, mostly!) My parents want to have a big family vacation at Disney with their grandkids...who can blame them!
Hmmmm...I may need to get the ball rolling on this....I need a Disney trip!