Hi Navy Vet,
In 2008, we flew to Denver and got on the Amtrak at Union Station (that is quite the experience)road to Salt Lake City. Then, we rented a car and went to Yellowstone, etc. We did the same in reverse a week later. I think you and your wife will love it. The people you meet in the dining cars and the sandwich shop are memorable.
The only thing I would change, is I would get a sleeping car. Otherwise you have to sleep in you traveling chair.
The observation cars really make the trip.
The best of luck to you and your wife, Navy Vet.
It is even more of an experience today. Union Station has been refurbished and is the transportation hub for downtown Denver.