You'll have no problems taking 20 into West Yellowstone and over Ashton Hill. It's a steep grade, but relatively short. Most vehicles make it over just fine.
Another route would be to take I-15 to 26 (instead of 20) in the Idaho Falls/Ammon area. Take 26 all the way to Alpine, then 89 into Jackson. If you take this route DO NOT turn off onto 31 to Victor, Idaho, or you will be forced to take Teton Pass down into Jackson. It's a long steep pass up and down. We did it once and never again. The I-15 to 26, then 89 into Jackson is easy all the way.