About 8 years ago we planned a trip from MI to Yellowstone / Mt Rushmore / back. We did it in about 15 days. Drove 6-7 hours each day - 4 out 4 back. We stayed at campground just off the highway at the 360 - 400 miles per day route. This gave us about 7 days. We saw what we needed at Yellowstone in 4 days ( yes could have spent more). 3 days in the Mt Rushmore area.
We enjoyed the trip across the country as much as the destination. There is no way at my age now I could drive 4 days those miles. I would be worn out.
Sounds like your a little younger. Might work for you. But doing a longer drive each day would probably get you more time at your destinations. To keep driving with no downtime isn't any fun.
If I had the time to do that trip over again it would be 3 or 4 weeks. But if you have others to spread the driving around, and a young man to see the great country. I'd find a way to make it work.