We drive a lot, 2 kids, road trips, but I can't imagine that marathon run especially with your wife's mother in law playing backseat driver, lol!
IMO you're not going to get much out of the trip with only 3-4 days of vacation. Plus you'll be missing everything else you should see in the southwest and Rockies.
If you cut all the stops short you'll still only make maybe 50mph avg. not like setting the cruise at 85 or 90 running bobtail.
The other concern is getting campsites at either park now. Have you looked in to it?
Destination spots like GC and Yellowsotne are usually booked a year out.
I'd say doable, but overly ambitious in a week.