Driving from Michigan I would focus your time left at Yellowstone and Teton area and not rush. It's a lot of ground to cover and they are close together. We just did this trip end of last June via flight, rental car and lodging. Stayed in Jackson couple of days, then a few at Headwaters Flagg ranch, then a couple days in West Yellowstone. Flagg ranch had hook up sites, west Yellowstone has Grizzly Rv park. So much to see and do. Book now, in park lodging was not available when I called last January to book in June! But they may have campsites within parks available.
