If the Tetons and Rushmore are your two priorities, have you considered visiting one on the way west and the other on the way back?

It would be quite a bit easier just to take I-80 all the way into Wyoming and then head up to the Tetons, then continue onto Oregon by heading out towards Idaho Falls.

On the way back, you could stick to I-90, which would take you right to the Black Hills, so you could easily see Mt. Rushmore.

It would save you time and miles, and give you the chance to see different things on your return trip.