First of all, I object to calling your trip and wish list "Disney." If you want to go to Neuschwanstein, go to Neuschwanstein! I did, on my first trip to Germany when I was 21. My dad and I did one of those day-long bus tours on a rainy day. We saw Lindhof, Neuschwanstein, and stopped in Oberammergau. Were we with a bunch of other tourists? Yup (in fact, we met people from our home town!). Was it crowded? Yup. Did I love it? Absolutely. Do what interests YOU, and if that means castles/palaces and WWII, then do that. Love the Sound of Music? Take the tour! I've been twice, because it gets me up into the mountains. It's corny as heck, but I love it. My cynical sister even sang along when we went. There's also a luge ride, which - how can you say no to that? My point is don't let the fear of doing something "touristy" stop you from doing what you want.
Okay, with that out of the way, two quick questions: Are you meeting your family in Prague, or in Munich, on June 10? That is, do you need to be in Prague on June 10? And, is there anyway to change your ticket to leave from Prague?
Either way, I think you're going to need to cut Vienna. If you're absolutely married to Prague on this trip, then one of the big cities has to go, and my suggestion would be Vienna.
Nürnberg has an excellent documentation center and party grounds, since you're interested in WWII. It can be done as a long day trip from Munich, if you'd prefer to stay in one place longer. Salzburg has disappointed me both times I've visited, but that's my personal opinion, and if you are interested in music and Mozart, you will probably get more out of it than I did. That can also be done as a long day trip ( I think both Salzburg and Nürnberg are about 2.5 hours from Munich by train. Again, long days, but technically doable).
What if you did:
6/4: Arrive Munich, work off jet lag.
6/5-6/9: That's five full days to explore the city and take any day trips, either out of town, to the castles (palaces), or into the Alps.
6/10: Travel to Prague. (I saw on the DeuscheBahn website a direct train that gets you there in 5.5 hours. Others have also suggested a bus. I'm not sure on price for the train.)
6/10-6/13: Prague. That's 3.5 days in Prague, which should be doable.
6/14: Travel back to Munich.
6/15: Travel home.
You won't get to do EVERYTHING on your list, but if you drop Vienna you'll be able to do a lot. And don't worry about Prague. It's very tourist-oriented, so language won't be an issue. I don't speak a lick of Czech and never had any issues. It's a beautiful city.