Anything directly from the Black Hills to Yellowstone is going to have twists & turns because it's crossing the Bighorn mountain range. If you want to avoid that, stick to I-90. More miles, but much flatter. You WILL have some twists & turns going into Yellowstone from almost any entrance except the west, and once within the park there are some as well, though nothing as extreme as you'd encounter in the worst of mountain driving. (The Bighorns are worse than YNP, trust me.)
You might consider doing a search on this forum about Yellowstone & Black Hills - there have been a ton of people asking about these routes, and just about as many answers! :)