Yellowstone or bust

I can't believe I'm saying this, Yellowstone being my favorite place on earth, but you might shave one night off Yellowstone and spend a little more time getting to/from Glacier. Between the 2 parks is a Looooooooong way - more than you might think, especially since driving through Yellowstone is not a timesaver. (You have no choice with this, though.) I'm not familiar with the route between East Glacier (Browning) and YNP territory, but if you were heading to the west side of Glacier, a good partway stop would probably be Missoula (Jim & Mary's RV Park looks nice from the road & gets good reviews).

I definitely like the Devils Tower KOA suggestion. I'd make reservations - they could fill up if you're getting there after a long day on the road.