Suggestions on our itinerary

First, I would advise you to mark how many nights you spend in each place, rather than days. It gives you a more accurate idea of the amount of time you have. For example, you have 3 days listed in Dresden, but really, if you are getting there on the 7th and then leaving on the 10th to go to Nuremberg, that only gives you 2 full days (3 nights) there, since the day getting there and the day leaving will both be tied up a lot with driving.

That said, it's probably enough time for Dresden. It might be a bit tight when you get to Nuremberg, as it looks like you are arriving in Nuremberg on the 10th day and then leaving on the 12th. This gives you two nights in Nuremberg, but really it's only one full day, so either Rothenburg or Nuremburg will probably suffer a bit. I mean, you can always see part of Nuremberg on the day you get there, but I would imagine that you would be leaving early on the 12th, so that really only gives you maybe a day and some change.

And again, you've got 5 days for the Rhine and Moselle valleys, but really, if you're staying there from the 17th and leaving on the 21st, that only gives you 4 nights and therefore 3 full days there. That's certainly enough for that area, I think, but it's easier to be realistic if you are realistic with your dates.

Also, your itinerary is a little confusing. Are you taking the train to Berlin right after you land in Frankfurt? And just out of curiosity, why aren't you flying into Berlin? You could fly into Berlin and out of Frankfurt using a multi-city option when you book. I would strongly suggest considering that option. It's usually not much more expensive, and when you factor in the time involved in taking the train from Frankfurt to Berlin and the cost, you're probably looking at at least, at the very least, breaking even but possibly even saving money.

One other thought. Depending on where you're staying on the Rhine, Heidelberg is actually close enough that you could potentially do it as a day trip, which would save you from having to spend one night in a place and then moving on. That always adds time that could be better spent sightseeing.

Not rushed

Good selection of destinations for history museums and a good pace imo.

Rental car for Nuremberg and Munich makes no sense. Use widely trains and public transport. I would earliest rent one when leaving Munich. For rental car you will likely need IDP (regulation).

You will miss the Northern part of Germany with own history, e. g. Vikings, Hanseatic League, own impressive architecture style Brick Gothic, and some interesting WWII sights such as submarines. I will not recommend to change plan because you have to prioritize and spend time at destinations.

A few comments:

-- I wouldn't rent the car until you reach Nürnberg. The train between the two is just about as fast, and if you're not planning on making stops midway, why make life harder for yourself? Public transit between Nürnberg and Rothenburg is possible but involves multiple transfers, though, so the car would be helpful to have by that point.

-- If you're visiting Tübingen and want to see some other nice small towns nearby, you could do a loop Herrenberg-Calw-Weil der Stadt-Magstadt-Tübingen. Or, for a more scenic drive from Tübingen to Heidelberg, you could do Tübingen-Herrenberg-Calw-Bad Libenzel-Pforzheim, and pick up your original route. Or stop by Speyer on the way between Karlsruhe and Heidelberg, which is definitely worth a visit.

(Edited to add: Pforzheim is not scenic and not worth a stop! I only include it to give you an indication of the driving route.)