Hi, I've visited Yellowstone many times over the last 30 years or so. I took my 34' foot MH towing a Jeep Cherokee over the road between Mammoth and Madison Junction last year. There was some construction that added about a 1/2 hour to the trip. Other than that it is more than adequate for your RV with toad. I've also driven the road to Gardner from Mammoth and while steep 7% for about a mile the rest is good.
See this: https://www.nps.gov/yell/planyourvis...nstruction.htm
I see where there are currently no construction between Madison and Mammoth but the map shows there are delays between Mammoth and Gardiner. I can't imagine that they will be long enough to offset the extra 100 miles!
Also see: https://www.mdt.mt.gov/travinfo/construction.shtml
Scroll down to US89. Whatever construction in Montana must be completed. No mention of construction near Yellowstone.
You might inquire with a Park Ranger. They will have the latest news. Many of the Park staff stay in Gardiner and drive the road everyday. 18 Wheelers come up and down that road making deliveries in the Park. They are much bigger than you!
I think I would just GO! You might just see something interesting along the way. Isn't that why you are there?