For the first, a car is best. Take Hwy 27 south from Stuttgart to Hechingen first. Hohenzollern Castle is just on the other side of it off of the highway. After your visit, return to Tuebingen and visit the old town. Then drive to Bebenhausen Monastery. After visiting it, continue on in the same direction to Waldenbuch. It has a nice museum of everyday life in the palace which you won't have time for, but the Ritter SPORT chocolate factory is off to your left. They have a small museum on chocolate manufacture, a larger museum on art in the form of squares (their candy bar shape), and a large sales room at discounted prices. Continue on then to Echterdingen where you can get on the B27 freeway to Stuttgart.
The second day, I would use a 3-zone group ticket for public transportation. If you think that you will stay in the automobile museum longer, than drive. Just take Hwy27 north to Ludwigsburg, which will pass along the west edge of the palace. Turn at the corner before it to the right, and then just after the gardens to the left where you should be able to find a parking place. There is an entrance down this road. Besides the excellent palace tour, there is several days' worth of things to see. I recommend the fashion museum which has lots of clothes from the 1700s, and also the gardens including the Fairytale Garden.
By public transportation, when you leave the train station in Ludwigsburg, the buses are to the right, otherwise it's a 20 minute walk to the palace. These buses are included on your group ticket. Oh, at the gardens bus stop, go down that same road as if driving and parking, otherwise its a several times longer walk through the gardens and you'll end up at the same place.