Welcome to the RTA Forum!

I'm a little concerned that you are trying to do so much in a short time here that driving very much will suck some of the fun out of this trip.

Your first day alone would be more than 850 miles, that's going to put you on the road for upwards of 16 hours. That kind of distance is even more than we advise for a speed run, and certainly isn't condusive to an enjoyable trip. I understand wanting to cover some extra ground on day one, but right now, you're going to wear yourself out before you even make it out west.

Even your second day is overstuffed. Driving from Sioux Falls to Rapid on one day isn't too much, and you can fit in some siteseeing during the day, but to try to fit in the Corn Palace, Badlands, and Mt. Rushmore plus the 400 mile drive, would be a ton of stuff to shoe-horn into one day - especially after your intense day one.

Giving yourself a couple of days at Yellowstone and in Colorado seems like you'll be fine, but also remember, you're looking at full day drives from the Black Hills to Yellowstone and another very full day back to Denver.

You can probably do everything you've listed that you have planned, but I think you're really going to be exerting yourself to do it, and I think you are in danger of having the driving and an overfilled schedule taking away from the enjoyment of your trip.