Can't say whether or not Stuttgart's a "must" for you, but if you are going to visit I'm not sure what you would do for only 2 hours other than drive through it. It's a huge city with almost 2.5mm people in the metro area, and will be different than a lot of the smaller towns you'll pass through. There's a lot more to do besides visiting museums and churches; there are plenty of festivals held through the summer, especially in late July and early August, as well as plenty of theater and performances that your wife and daughters may enjoy. I would do a little research to see if there's anything that tickles your fancy.