Rick Steves has a recipe for putting together an itinerary. Maybe you have seen it: https://www.ricksteves.com/europe/germany/itinerary
I don't think the destinations he suggests are necessarily "the best" way to get a first impression of Germany. The best itinerary for you should probably include one or two elements that you and your daughter are the most interested in. But I'm unsure what those might be, so my suggestions will include some guesses about that as well as my own ideas.
My guess: you have a strong interest in places with old-world character (Rothenburg, Heidelberg, Rhine and Mosel Valley towns) and natural beauty (Alps, Alpine towns/Garmisch-Partenkirchen, Rhine and Mosel Valleys) and in castles (Neuschwanstein, Rhine and Mosel Valleys.)
Like the others, I think your 10-day trip may be too rushed. It's not easy visiting a new country on an itinerary that is too tight, and it might just be less fulfilling as well if you end up spending too much time traveling. So I suggest you do some trimming. Here's what I would keep if I were giving my best advice to my best friend:
Day 1: Fly into MUC airport. Stay one night nearby. Take the train into Central Munich (45 minutes) or to Freising (10 minutes) depending on whether you want a big city or small town stay. The point after an overnight flight is to just tend to your personal needs and get adjusted to the new time zone, stretch your legs a bit, MAYBE see something, get a meal and a good night's sleep if possible.
Day 2: Train to MITTENWALD for 2 nights. 2 hours from Munich or 2+ hours from Freising. The train to Mittenwald stops in Garmisch-Partenkirchen on the way. Mittenwald is the quintessential Alpine town, much more walkable than sprawling Garmisch-Partenkirchen. The Karwendelbahn Mountain lift, the violin shop/museum, the Leutasch Gorge, and the old town itself are terrific.
https://www.tripadvisor.com/Attractions-g187300-Activities-Mittenwald_Upper_Bavaria_Bavaria.html
If you wish to see something specific in Garmisch-Partenkirchen, you can make time for that; either 1) get off there on your way to Mittenwald on Day 2 (put bags in a station locker while sightseeing) or on Day 3 take a short train ride (20 minutes ) there and back from Mittenwald.
Day 4: Train to NUREMBERG for 2 nights. The train trip from Mittenwald takes 3.3 hours. This is the "big city" you should visit because its old town zone feels small and adorable, just as Rick Steves says: https://www.ricksteves.com/europe/germany/nuernberg
I do not place a big priority on visiting the Nazi-era things that Rick is so enthusiastic about. Perhaps you will. But the great thing about Nuremberg is that there are so many OTHER things to see and do. And Nuremberg has its own castle too, right in town.
https://tourismus.nuernberg.de/en/discover/places-of-interest/kaiserburg-imperial-castle/
https://tourismus.nuernberg.de/en/discover/places-of-interest/
https://tourismus.nuernberg.de/en/discover/museums/
Day 5: Train to ROTHENBURG for 1 night. The train trip takes only 1.25 hours. Rothenburg is small and does not require a lot of time. My choice would be to stay an extra night in Nuremberg and visit Rothenburg on a day trip. But my opinion is in the minority - most people will tell you that you have to sleep there to enjoy the town fully, and Rick does the same, so...
Day 6: Train to BOPPARD for a 3-night stay. You need 3 nights here because of the 4.5 hr. trip to get there on Day 6 plus the trips you will need to make in order to see the area. Burg Eltz + Cochem. Marksburg Castle + Braubach. These are the true medieval castles which are worth your time and your tour dollars. Ehrenbreitstein Fortress. Bacharach. The Rhine Cruise. Use Boppard's free VRM Guest Ticket for free train travel while there.
Day 10: Train to Mainz for a visit there and your final night. From Mainz you are just 20-25 min's from FRA airport.