If you have a drivers license and can rent a rental car, do it on your own term and schedule and save a lot of money. The Amtrak stations are nowhere near those parks so you are at their mercy on their buses.
I would do it independently simply for the choice of restaurants instead of the mass prepared food with the tour company.
The most beautiful National Park I know of next to Amtrak is Glacier.

There are no train tours - the trains don;t go there. There are bus trous run by tour companies and bus tours run via Amtrak (which is usually late).

For the Amtrak tours lokk into the details carefully to see how they work the train and bus thing.

Agree that car is the way to go.

Thanks for your responses. I don't have a whole lot of time to research and plan this trip, which is why I was looking to go with a touring company. As we would be flying out of Michigan to see these sights, where would be the best city to fly in and out of? From what I've read, to avoid the peak crowds and kids, September seems to be the better time to go. Since this area seems to be a major tourist attraction, would winging it and making hotel accommodations from the road a couple days ahead be sufficient to find a decent room, as I've read to stay at Old Faithful Inn, you need to make reservations months ahead of time? Also, how is the driving in that area, as I really don't like driving curving, mountainous roads? Really appreciate your input!

If you feel you must fly instead of just driving an extra day, fly to Minneapolis (MSP) and rent a car from there.
Depending on where in MI you live I would drive to Rochester Minnesota the first day and to Rapid City SD the second day.
The third day I would see Mt. Rushmore and maybe some of the Badlands or the Crazy Horse Monument. The lodging in Rapid City will probably be cheaper. Next day (4) leave Rapid City and head for Cody WY seeing Devil's Tower on the way.
If you can get lodging at Old Faithful-good for you. Otherwise you should make a reservation at a place in West Yellowstone Montana. The driving distance from Detroit to West Yellowstone via Cody is about 1850 miles.

I did a two-week bus tour via AdventureBus, the second week of which went to Yellowstone, Grand Teton, and Jackson, WY. If memory serves, this company has a separate tour that covers Mt. Rushmore and other South Dakota sights. What I liked about AdventureBus was that getting out and hiking was very much a part of the experience, but don't expect a "sleep in a hotel" experience, more a camping-style approach. I did enjoy the trip. Their website is here:

http://www.adventurebus.com/

There are other companies that do tours of this kind. See this earlier thread on this forum:

http://www.fodors.com/community/united-states/travel-dream-west-tours-of-yellowstone.cfm

Driving strikes me a a good way to do a trip of this kind if you can do so. It's not an option for me, though.

I shall be leaving for a trip of national parks starting in Rapid City, SD, ending in Denver, for 18 days. Travel is by bus, which is why husband won't go. I have traveled internationally with this company on 5 previous trips and we are most pleased. It happened to be on a last minute sale so I feel it is a good value, but if husband wanted to take this trip it most likely would be cheaper to rent a car rather than each of us paying for the same hotel room. You may have heard of the company, Grand Circle Travel. Here is the link to the tour:

http://www.gct.com/Trips/2012/Americas-Majestic-National-Parks-2012.aspx

Karen