Your trip looks pretty good overall, but you will be spending lots of time in the car. Driving is slow in the Black Hills. It will take you much longer to get from place to place than you would think from looking at the mileage.

One thing I didn't see specifically mentioned, but I would highly suggest would be the Needles Highway. This is in Custer State Park, and would be best on the day you see Mt. Rushmore. Also, 1 of the caves would probably be enough (Jewel is my favorite)

I have not been to the Mammoth site or the horse sanctuary. Also, I would do the Badlands and the missle site on the same day.

Sorry for the randomness of this post - hopefully you can follow it. Let me know if you have any other questions.