Pjracer, this adds to the post Alan linked.
Walkers are a little different than wheelchairs, but the information is similar. Folding, rigid, or one of those large wheeled things that you can sit on? How thick is it when folded (has to do with where they need to fit it if you get a regular room instead of the H-room). Is it so light it can be lifted anywhere?
Say "yes" to do you need help, plan to tip for good service, even lousy car attendants generally give good service to nice people with disabilities. Let them know whether you'll want the ramp or lift. Unless you are really good with large steps up, I recommend asking for the ramp/lift, then decline it at the time if the step isn't too high for you.
One thing to note about the H-room is one bed is low but one is high, so someone is going to be crawling up a ladder. If neither you nor your wife can manage that, then you might consider two roomettes across the hall from each other (for daytime views out both sides). That worked real well when traveling with my mother (and her scooter and walker). I've also slept on the floor in the H-room (costs a lot less, I'm cheap!). If you want to consider fitting two people on the lower mattress, ask about that in another thread to see if it'll work, I think it depends on the exact type of car and room, and your sizes.
The handicapped room is very easy to reserve, they save it for people with mobility disabilities until two weeks before departure. However, price follows roomette buckets (learn about them elsewhere if you haven't yet) so reserve as early as you can. The 15% discount is for person with disability and up to one helper, and you can get it on other rooms/seats, too.
There are other acceptable identifications besides doctor's letter, Amtrak lists them somewhere on their disability page. Your parking placard and its registration will work fine.
Enjoy the trip!