I did it a few years ago, from MI to Yellowstone and back. I would leave at 3:00 a.m. drive for 12 hours. Kids and wife would sleep in car until about 9:00 or 10:00 a.m. We would then stop breakfast, and continue on to a RV park. Plan on get to the RV park by 3:00 p.m. Kids and wife then would play, swim, sit around the campfire, play board games, whatever, until about midnight. I would go to sleep at about 8:00 p.m. We left the trailer hooked to the truck and only plugged in the electrical (make sure you got a pull through site). At 3:00 a.m. load kids and wife in car, unplug, pull out and do it all over again. By the third day everyone is whipped but I would do it all over again.
Got to make all your reservations for stops ahead of time. We stayed at Albert Lea, MN (this was a 13 hr drive); then a few days at Custer State Park, SD; before continuing to Yellowstone on way out. On the way back we stayed in Cheyenne, WY; Des Moine, IA; then home.
By leaving at 3:00 a.m. the kids are mostly only sleeping in the car, are awake for about 5 hours. Then they get to the campground where they get to play at the campground for about 9 hours then go to sleep.
I would suggest breaking up the trip on the way out and stay for 4 days or so in the Mt. Rushmore area. Then continue to Yellowstone.
