We got to Stuttgart safe and sound, and rented our car. Although it took about an hour to find the rental agency because we walked right by it as we got off the train and didn't double back far enough when searching for it.
Getting out of Stuttgart and onto the correct highway to take us to our destination was a bit tricky. The motorways and exits around central Stuttgart are a little convoluted, and we were just learning how to read the road signs. After another hour of randomly changing directions, we finally got headed in the right direction on the motorway.
We eventually ended up on the right highway into the hills, and after asking directions at a gas station (yes, even the gas station employees spoke enough English to help us), we came to this gorgeous five-star hotel nestled on a hillside.