Traveling with a toddler is fun but you need to remember to relax your pace a little bit and be prepared to adapt to their moods. We've been to Europe (mostly southern Germany) many times with our two who are now 4.5 and 2.
Your plan of having a nap in the car after lunch is what we have often done. Usually it works ... sometimes not so well. Snacks are critical. I always have a bag of snacks and drinks with me (you will find fewer pre-packaged toddler snacks like granola bars, rice cakes, etc in Europe). I usually make a peanut butter sandwich each morning to take with us, too. The kids eat pretty much everything but there is something about the familiarity of a PB sandwich that can really tide them over when it is close to lunch and we want to see a little more of something 'boring'.
I strongly recommend taking your own car seat. It is a bit of a hassle but well worth the peace of mind - I did a lot of research before deciding to do this on our trips but I wasn't willing to take the risk of getting a seat that had been in an accident or not getting one at all. I strongly recommend getting a bag (we found one with backpack straps for CDN $35 on Amazon) to protect it, too. We didn't on our first trip and the seat got pretty beaten up on the flight over. At 2.5 I'd also suggest taking a good stroller, you may not always need it but will be glad for the times when you do.
Try to break up your mornings and afternoon with toddler-friendly things. You know toddlers, these don't have to be a big deal. My kids especially love chasing pigeons and splashing in fountains. Find out where the playgrounds are and make a point of spending half an hour there just for her. We have found many towns actually had pieces of playground equipment in the middle of the main squares, too. Most towns in Southern Germany have ice cream cafes (Eis Cafes) and these make a fun stop for everyone - ice cream for your daughter, espresso for the parents.
Many Biergartens have playgrounds right next to their outdoor seating, which has been a lifesaver when we wanted to have a leisurely lunch and an extra beer.
For a pretty, mostly medieval town, I recommend Schwabisch Hall. It is a little off the beaten tourist path, has a lovely old town centre with pedestrian zones where she can walk without fear of cars and a great playground very close to the town centre right beside the river. We had a fun encounter here with a fruit vendor - my son stole a peach from her stand and when I made him take it back she smiled and gave him an apple instead. It made for a fun story and another great memory!
I've had people say you should leave the kids behind because they will just take away from your trip. I disagree. Taking our kids can be a bit more challenging - we see less museums and more playgrounds - but it has always been enriching. We meet a lot more locals and have learned to slow down and savour each place instead of just checking off a list of 'must sees'.
Have fun and feel free to PM me if you have any specific questions.
P.S. We've taken Russ' suggestions on several trips and they are always good.