You can easily get from Prague to Salburg via Linz by train. It's faster than going thru Vienna. I've done both routes, although the last couple times I was over I drove in the opposite direction. For Prague to Munich the fastest way I know is via Nuremberg.
In Salzburg take the teenagers to the Red Bull Hanger 7 just outside the city. Even better, check the schedule and see if the team is playing locally.
From Salzburg to Munich is less than 2 hours and the scenery is pretty good. It goes fast.
In Munich I've never met a kid of any age who didn't like the Deutsches Museum, which is all kinds of "how to" displays for building almost anything, and has an underground mining tunnel that runs under the river. Usually it's the parents who are ready to leave first.
There's also the Observatory if they like stars and space, and I can't imagine them not enjoying the BMW museum more than Oberamergau (which is going to be packed stupid this year due to the Passion Play.)
You should seriously consider a visit to Therme Erding, a combination of swimming park and spa, and a cultural experience for American tourists. It can get crowded, but there are smaller ones around that are less so. Try: https://www.kristall-trimini.de/ or https://www.swm.de/english/m-baeder/sauna/prinzregentenstadion.html
Munich also has Octoberfest, and while you're not going to be there at that time, your teenagers should know the legal age is 16, and they can go into any of the beergardens (family's are welcome) even if none of you drink. That's a great "one up" on what their friends are doing.
Everything I've mentioned is easily done without a car.
Last, there's no way I'd go to Fussen in June. Or Oberamergau anytime this year. Or to the castles down south. Those destinations are going to be jam packed with tourists. Do what the locals do, hit the open markets (Grunmarkt in Salzburg, the Victualmarkt in Munich), walk the streets, sunbath in Munich's English Gardens or on the river bank in Salzburg. Sit and drink a beer, eat some cheese and meats, and watch the world go by. Both Munich and Salzburg are major University cities, let your kids have time to interact with the locals; I can think of no better way to get them interested in further travel.
