Shiela,
I too use a walker. If you have the H-room on a Superliner, there will be no problem. In coach, the lower level also has a handicapped rest room. However, all access to other cars (Dining Car, Lounge) is via the upper level only.
In a Viewliner (single level car), the H-room has an enclosed (with a door) rest room and shower. The entrance to the room is a direct straight line from the vestibule. However, the walker will not fit down the hallway or in 99% of the coach cars. Except for seating at one row at the end of the car, and at least one of the rest rooms in each coach.
If he is able to walk short distances (as I can), it is possible to move around. I use the walls of the sleeping cars, the "candy stripe" handrails between cars and the seatbacks for support. (As should everyone!)
Enjoy your trip!