I just entered Yellowstone from Cody WY US 14/16/20.
This road is driven by all types of vehicles with much longer trailers than yours. Tour Buses and Tractor trailers. My trailer is 33 overall. This is a fine road. NO Problem.
Also it is one of the more scenic routes into the park.
Currently the road from the northwest entrance (Gardiner/Mammoth)into the park is under construction and the delays can be horrendous. Avoid it.
I also entered the park this year at West Yellowstone. It is easy yes but the least scenic. And if you are coming from the east there is no reason to go all the way around.