It's tough giving advice without knowing your focus and what your goals are. We just got back from the South Dakota area. What you are planning is going to be lots of driving and backtracking. My advice is Wall drug, half day. Rushmore half day. See devils tower on your way to Yellowstone. The major attractions in yellowstone are located on the figure 8 roadway inside the park, and will take at least 5 days. Tetons are south and 2 days to see those attractions. Most people do not realize how much driving is often involved in all of these areas. In the summer, you need to add in massive traffic volume. And in yellowstone you need to stay flexible. It is not unusual for animal stings to back up traffic for 20 to 40 minutes. Enjoy your trip.
