Germany trip adding Prague

You seem to have left something out. Do you mean drive to Salzburg from Munich, which is a common choice? This trip does not go into Czech Republic. You always need to ask at the pickup desk, but Austria is not often a restricted country for car rental.

I happen to find Dresden a very attractive destination, in many ways nicer than Munich. It is convenient to both Berlin and Prague. (Opinion) I only mention something you don't want to do because it is so close to Prague. I am sorry that I did not go to Prague earlier in my travels, so I certainly approve of adding Prague to your trip. We trained back to Berlin from Prague some years ago.

A short trip to Salzburg doesn't really need a car, and the train trip from Munich is very easy. You certainly don't want to drive around Salzburg, but I know some people are determined to drive the nearby countryside.

this our plan.
1 Frankfurt? or 1 hour drive to bacharach
2 Bacharach - Rhine Valley
3 Bacharach
4 Baden Baden
5 Baden Baden
6 Freiburg or Stafen
7 Bavarian Alps - best by car
8 Bavarian Alps
9 Bavarian Alps
10 Salzburg
11 Salzburg
12 Munich
13 Munich
14 Munich
15 Rothenburg
16 Rothenburg
17 Nurnberg
18 Nurnberg
19 Prague
20 Prague
21 Prague
22 Berlin
23 Berlin
24 Berlin
25 Berlin

Do we drop the Car in Nurnberg, train to Prague and then train back to Berlin?

Yes, it can be done as you suggest.

It would be your rental car company which decides where its cars are permitted to drive.

I do not recommend Rick's suggested itinerary. It's too hectic and you will miss too much:

https://www.ricksteves.com/europe/germany/germany-map-itinerary.jpg

1) There are too many miles in this bus-trip-paced plan. In some places you simply will not have enough time (1 day for the Rhine Valley + half a day for the Mosel Valley, for example... not enough time in the Alps...)

2) Driving into Munich, Salzburg, Nuremberg is never a good plan.

Specific suggestions for adjusting Rick's itinerary: This is still very rushed, but it will include most of what you want and Prague too.

Assuming that you want to drive... I suggest you use the car for the first half + as far as Salzburg (Freilassing, Germany,) then drop it. Use trains for the rest.

• 4 nights for FRA airport > Rhine/Mosel Valley (adapt to the new time zone (jet-lag) and include Trier, Bernkastel, Marksburg Castle.) You don't have to stay in Frankfurt; catch a train to Bacharach (or a better Rhine Valley base town) and get the car on Day 2 in Koblenz so that you aren't driving jet-lagged, drowsy, etc.

• 1 Night in Rothenburg (Drive there)

(DROP Baden-Baden, Freiburg, neither of which is really in the Black Forest anyway.)

I would NOT drop the German Alps, as it appears you've done. Drive to the Alps via the Romantic Road or hit other nice towns of your choosing.

• 1 nights in Füssen (Drive the Romantic Road to get there) but only if you are sold on seeing Neuschwanstein/Hohenschwangau)
• 2-3 nights elsehere in the Alps - Drive to Highlinge 119?, the Zugspitze, then to Garmisch-Partenkirchen, Oberammergau, or Mittenwald. Do some alpine lifts, walking, river gorges, etc.
• 2 nights in Salzburg - Drive to Freilassing, drop the car, catch the train into Salzburg.)

Then by train...
- 3 nights Munich, including Day Trip to Dachau (Drop Nuremberg)
- 3 nights Prague
- 4 nights Berlin

EDIT: OK, I see you actually have already adjusted Rick's plans and added 5 nights to Rick's 3-week trip. So YES, do include NUREMBERG and use those nights there. I would insert Nuremberg into the plan I suggested right after Munich. Train from Munich > Nuremberg > Prague > Berlin. Nuremberg is a terrific travel base town. Take day trips from there to your choice of nice places... Würzburg, Bamberg, Regensburg, Bayreuth, Iphofen, Bad Windsheim, and others. You can just play this time and these outings by ear in Nuremberg.

Your trip is still 5 months out, and I would spend a little time researching alternatives.

I like the amount of time you're giving places. I think you need 2-3 days to really have time in all the locations you're aiming at. But I'd make a couple adjustments. I'd stay in Mainz and visit Bacharach and the Rhine Valley because this is going to leave you a very noticeable distance closer to your next location. And there's no way you're going to drive from Bacharach to Baden Baden in less than 5 hours in July. Maybe early on a Sunday morning, but otherwise traffic is going to make this a long day on the road. From Mainz you'll save close to two hours.

And I prefer to stay in Freiberg over Baden Baden. It's less expensive and I think there's more to see. But I'd totally pass both of those and go to Lake Constance, which is, by far, a better destination. And from there you're at the foot of the Alps (admittedly the Austrian/Swiss ones).