Need help with 10 days in Germany next month please

You can see most/all of those places by train without renting a car if you wish.

Consider doing your nights in Munich at the end so you don't have to split up your time there - and head to your first destination by train (or bus in some cases) as soon as you land. This will be easier if you arrive early in the day - not practical if your plane lands too late in Munich

Plot the towns you are considering a visit to on a Google Map just to see where they are (even if you aren't driving between them, it gives you an idea of distances). Bavaria and Salzburg are easy from Munich; Baden Baden and the Rhine are much further away and require backtracking as you are flying into and out of Munich (the Rhine would make more sense if you could fly out of say Frankfurt).

Salzburg is an easy day trip from Munich by train, but it's also a lovely town where you may want to spend a few nights on its own - up to you. (I loved it, and I'm not even a fan of The Sound of Music.) You could start in Salzburg after landing in Munich - that's what I did.

I also would do Munich at the end. I would do Salzburg a couple of nights, and somewhere in the German alps - Garmisch-Partenkirchen is a popular choice (its a resort town). You can get just about everywhere easily by train, so car is optional. Note as far as rooms are concerned, that European hotels' rates are strictly based on number of people, so that you can't necessarily get one room and have as many people as you want in it. Somebody else may be able to comment on the availability of four person rooms.

69, 55, 22, and 19. You didn't indicate the genders, but it sounds like two double rooms would work.

Outside of major chain hotels, most accommodations include breakfast with your room, so I guess that makes them a B&Bs. The closest thing to what Americans think of as a B&B would be what the Germans call a Privatzimmer, but these are harder to find with the websites usually used. Small Gaestehauses or pensionen are almost as good. Some people stay in Ferienwohnungen (apartments), especially with four people. Some have a bedroom and a sofa bed in the living room; others might have two bedrooms, but these come with kitchens and minimal services. You normally have to make your own breakfast from ingredients from a grocery store.

I wasn't too impressed with Salzburg, but nearby Berchtesgaden is an alpine beauty and, IMO, a must see.

There is so much to see and do in Bavaria, I wouldn't bother with Baden-Baden or Bacharach.

I've spent months in this area without ever needing a car.

We had a similar situation this fall. DH, myself and our two "kids" who are in their early 20's. We stayed in Munich for 5 nights at the beginning and had two rooms at Pension Lindner. The nice thing about two rooms is the kids would stay out much later than we did, and having an extra bathroom of course was very helpful. We loved the pension and the location was excellent. Then we took the train to Rothenburg for a few nights. We had the family room at Hotel Spitzweg. It was very large, with two sleeping areas. Even with one bathroom, it was very doable for us. This was our favorite hotel of the trip as it was so charming, and the host even more so. After that we headed to Salzburg for a few nights. I can't remember the name of the hotel. It was fine, but if we return I would opt for another, so that sort of tells you something, lol. We were glad we did not just do a day trip here as it is such an enjoyable place in the evening to just wander, plus there is so much to see in the area. Then we headed back to Munich for our last night, and stayed at the Hotel am Viktualienmarkt. We had one room here and it worked fine for us. The hotel is sort of sterile feeling, so no charm, but the host was wonderful and the location was excellent.

While in Munich, we did a day trip with Mike's Bike Tour's to Neuschwanstein. It included a short bike ride to Swan Lake, which was fun. That was a fun day and I highly recommend it! On another day in Munich, we just rented bikes from them and rode all over the English Garden and even way past the far end. We stopped at two of the beer gardens there:)

Another day trip was to Dachau. We did that in the morning and then the BMW museum in the afternoon.

Baden-Baden is a huge outlier here, and also IMO just an overrated place to visit. I'm not sure why Rick includes it in his book. The scenery in the Black Forest is not as great as what you'll see in Bavaria, so I'd skip that and not try to do the rhine on this trip. Focus on Bavaria.

How about you pick up a car on the 25th and drive to Bad Rechinhall, and use that as a base for visiting Berchtesgadener land (including Salzburg?) It's a spa town, like Baden-Baden, and has similar parks and buildings and you can take the waters if you like. I'd stay there or another town in that area (or in Salzburg itself) for 2-3 nights, then drive east, lots of places to visit along the way potentially such as King Ludwig II's palaces, and charming towns like Schongau and Landsberg am Lech which is a well-preserved medieval town. I wouldn't bother going all the way to Rothenberg. If you want a similar town, Nordlingen is my personal favorite on the Romantic road. From there, drive to Nuremberg, drop off your car, enjoy the city, then train back to Munich the next day.