I browsed the Dunraven Pass route in Yellowstone (google maps Streetview). Looks like the part that could give visual problems is where it follows a ridge above the treeline. It's not exactly steep, but the views are expansive. Reminds me of the high roads in Rocky Mtn Nat Park.
22, Teton pass has similarly expansive views, though the area is lower and forested.
If your driver was comfortable with Dunraven, then driving Teton won't be a challenge.
After Jackson and GT, you might want to use US191 to head SE toward I80.
