After I removed all of the screws, I pulled the old vent out and then cleaned the opening removing all of the old putty tape.
After I cleaned off the old goop and putty tape I scrubbed the area with steel wool and then cleaned the area with rubbing alcohol. Then I positioned the new vent in the opening and marked where it would be centered. I drew around the vent flashing with a marking pen. That mark also allowed me to position the new putty tape.
I positioned the new putty tape inside the lines I had drawn with the marking pen. I overlapped the tape in the corners and squished it together with my fingers.
I attached the new vent using #8 by 3/4 sheet metal screws. The wood was perfect in the framing and the screws went in well. Next I need to go around the edge of the flange with a sealant I got at the RV place. I'll do that tonight.
Here's what it looks like from the inside. I left the original metal interior trim in place and didn't use the plastic one provided with the new vent. I think it looks more retro with the metal interior flashing. Aristocrats seem to have this wire for lighting going along the walls and ceiling. My parents Aristocrat had this same sort of wiring also. Anyway, now I have the vent and rear window fixed. There's still more work to be done, but the only thing I really need to do now is fix one of the window screens and we will be able to use the trailer for our vacation in Glacier.