I know opinions vary but I would drop Mt. Rushmore for time. It's nice if you have time but if this is a once in a lifetime trip West, that's something to cut in lieu of the Grand Canyon and Yellowstone/Grand Teton. Custer is great if you can't get to Yellowstone but YNP has the wildlife, plus. I didn't check the route. If Rushmore is on your route from IL, drive through for the morning to see it and keep going. YMMV.
Arches in Utah is worth a quick drive through since you are doing the Grand Canyon and Bryce Canyon. There are tons of Yellowstone Threads but you need 4 days there, 3 in YNP and 1 in Grand Teton. Not optimal but doable.