Robbie,
I assume that you will be staying in Cass? If so, you can drive to the end of the parking lot and walk to the shop. There are signs that discourage you from visiting the shop, but you can walk to the water tank, and watch them getting the locomotives ready for the runs to Whittaker and Bald Knob. I don't know if Earl will be there on Tuesdays, but as long as you stay out of the way, you won't be disturbed. If you want to go into the shop, you need to have someone point you to Rex Cassell, who is the shop foreman, and get his OK, as the shop is quite active. If Earl is there, he will be running the Whittaker turn or simply doing paperwork in the shop.
Unfortunately for you, D&GV's other trains do not run Monday through Wednesday. They run the Climax at Durbin (which is a sweet little engine) or trains north out of Elkins and south out of Cheat Bridge. If you go to Elkins, there is a great restaurant in the depot there, and there is a forestry museum and the West VA RR museum in a building about two blocks south of the depot. Both museums are pretty new but they have some interesting things to see.
Be prepared for the fact that you won't have cell phone service for about 40 miles in any direction from Cass. The big radio telescope at Greenbank (8 miles from Cass) cannot have interference. I don't know if they give tours there or not but you can see it from the road into Cass and the road from Cass to Durbin and it is pretty impressive although not a railroad thing.