Can't remember if there are hairpin turns, but there are a couple sharp ones. Large RVs do that route all summer long. So just take your time where you need to and you should be fine. It will get fairly congested in spots in Yellowstone. Terms like bear jam and buffalo jam are common. It increases your tension in a big vehicle. But remember it's the journey that makes the memories. Enjoy
I've driven it over a dozen times, but either just pulling a popup with a truck, or just the truck, or once in a Vette. But I see a lot of large 5th wheels and motor homes with toads.