Personally wouldn't recommend it for scenery. A few long hills between Maybell and Vernal, but no mountains. Only becomes scenic at Steamboat Springs, but then you are immediately climbing up Rabbit Ears Pass.
But the question is, if your wife doesn't like mountain roads, how are you planning to see Rocky Mtn. NP? You will have to drive over Trail Ridge Road, the highest paved through highway in the U.S. (12,000 ft.), to get home if you are coming from Utah. Or you will need to go all the way around through Denver or Ft. Collins and backtrack to Estes Park. Either way you will have to cross the Continental Divide over a mountain pass, with consequent long grades. Even the west approach to the Eisenhower Tunnel on I-70 has an exceedingly long 6% grade from Silverthorne to the portal. So, there is no way to see RMNP without driving mountain roads.
As for "hairy," if you are driving a tall pickup camper, you won't find many paved mountain highways hairier than the hairpins on Trail Ridge Road (US 34) in RMNP! It wouldn't be a problem if you are completely comfortable on steep, winding roads, but it sounds like your wife is not that comfortable.