You can't do this in 10 days. Which would be 9 nights, right?
Cesky Krumlov and Vienna are way off your route. Vienna would be a 4hr trip from Munich - and 4hrs backtracking to the airport.

From Düsseldorf you could go to the Mosel valley (less touristy than the Rhine). Many small towns and villages that should suit your tastes. 2 nights
Drive thru Alsace/Lorraine to the Black Forest.
Black Forest - is a big area. Most like the Southern part best, more or less the Titisee region. 2 nights
Drive along Lake Constance to Neuschwanstein and Hohenschwangau castles. 1 night
Via Linderhof palace, ettal monastery to Munich. Drop car. Do Dachau as a day trip by public transport. 2 nights

Now you still have 2 nights to add somewhere according to your likes. Or by diverting your route slightly, e.g. go thru Switzerland from Black Forest to Neuschwanstein.

Hello!

We actually have 10 nights. Currently contemplating flying out of FMM (near Munich) or Vienna.
Vienna is much more expensive for us to fly out of unfortunately but would suit our hopes in getting there.
As far as driving, that isn't an issue for us. We are used to very long drives.

The issue is not that you would not be physically able to do long drives.
But rather if you consider being behind the wheel a valuable part of your vacation for which you wish to minimize the time you actually have to visit sights or engage in activities.
Especially since you described yourself as "active", I don't know why you wish to make sitting in a car seat your major activity.

If you did your whole trip as you planned it with just one night stays at each location, it should work - technically. I simply would not know what to suggest to visit if you had that little time remaining to actually do stuff and see things.

When you fly out of Vienna, you will also have to add the often steep fee for cross-border one-way rentals re. your car.
Alternatively, you can drop the car in Munich as planned, and take the train to Vienna (where you don't need a car anyway).

Cowboy is right - your itinerary is not doable. You will spend most of the time in a car (a considerable part of it in traffic jams) and you will have no time to see anything.

The first day you should spend in Düsseldorf - it is a beautiful city. Make the short trip the Neanderthal - it is a picturesque valley with a breathtaking state-of-the-art museum of your ancestors and the history of mankind.

Between Düsseldorf and München there is so much to see - why planning time-consuming sidetrips to Vienna and Cesky Krumlov?

Instead of Cesky Krumlov, I would visit Monschau which is about 90 min. driving time from Düsseldorf. See this short movie:

http://www.youtube.com/watch?v=P8DXeL78ZSY

On the way, stop in Aachen, visit the cathedral from 800 A.D. where Charlemagne was crowned and have a lunch in the Postwagen at the wall of the medieval City Hall. Here a movie of the cathedral (Dom):

http://www.youtube.com/watch?v=vV8gLFNX_O8

The next stop might be Köln with a magnificent cathedral, world-class museums, Roman heritage and the chocolate museum.

Then you wind your way down through the picuresque Rhein valley. I recommend visiting the Marksburg in order to get a real castle experience.

http://www.youtube.com/watch?v=CJGfpqHIYLs

From Koblenz, you can drive up the Mosel valley. Burg Eltz would be another castle:

http://www.youtube.com/watch?v=CWN_EMpFhJw

If you are interested in Roman heritage, Trier will be a must.

From Trier take the Autobahn to the Northern Black Forest. Calw is a pretty old town and Bad Teinach is located in a scenic valley (however, the thermal bath will be closed in July due to renovation).

Drive in north-easterly direction to the Romantic Road. See the beautiful historic towns Nördlingen, Dinkelsbühl, Rothenburg and the splendid baroque monastery in Neresheim. After that, you won't miss Cesky Krumlov.

Drive southwards to Füssen and see Ludwig's castles and get an impression of the Alps.

Drive northwards to München and spend some time in the city.

It will be an itinerary packed with attractions, sights and experiences. And save Vienna and Cesky Krumlov for your next trip to Europe. You said you are in the late 20ties? You will do it.

As a person who loves Germany, I can only encourage you to follow the advice above. Get a car spend some time, take a backroad now and then.

Sounds like a fun trip. You will want to put pins in a map and decide what makes sense.

I'm not sure Summer is the time for wine festivals but you will find more of them in the Rhine / Mosel areas than Bavaria. Try the beer halls in Bavaria and the Tyrol. You can get your Classical Music fix in Munich or Salzburg (Mozart dinner concert at Skt Peters Stiftskeller in Salzburg).

When you are in the Fussen (Neuschwanstein) area you are a short drive from Wiesskirche, Oberammergau, Schlos Linderhof, Ettal Monastary, Garmish, Mittenwald. Then is is a fairly easy drive to Bertschesgaden an Salzburg.

We enjoy car tripping but we only use them when we are not in big cities where traffic and parking are a hassel. Remember that picking up a car at an airport or train station in Germany adds 19% to you bill.

A lot of good advice here. I'll add another bit: Buy a good guidebook or two. I use guidebooks extensively when I plan my trips, and I always bring one with me when I travel. They contain lots of useful information.

Rick Steves guides have little "maplets" which tell distances and travel times by public transportation and also by car. Other guides give mileage from individual cities to larger cities. For instance my Frommers guide lists distance from Potsdam to Berlin, Leipzig and Magdeburg.