That sounds good, but I would suggest that after (and not before) Mt Rushmore, you visit the Crazy Horse monument.
It is a work in progress (as it has been for over 80 yrs), but it is fantastic!
Also, if possible I'd recommend that you travel back from White Butte into the Black Hills via Spearfish Canyon Scenic Hwy. It is certainly in the top 10 most scenic hwys in the country. It is slightly out of the way, but not by much. And just in case you have extra time, visit one of the 2 NPS-run caves, Jewel or Wind Cave. They have great tours of each.
Are you camping or lodging? Do you have any idea where you might be staying each night?