2 weeks in July with teenagers

Yes, it is possible by public transport. Munich has lots to see, and has good city public transport to see it.
Salzburg is an easy day trip by train from Munich.
A possible second location in the Alps is Innsbruck.
Dachau is a suburb of Munich and easily reached by city transport. Very sombering..

As a "primer" on how to do this by public transport (trains)
Start here (Germany): https://www.seat61.com/Germany-trains.htm
And here (Austria): https://www.seat61.com/international-trains/trains-from-Vienna.htm

Munich (München) is the capital of the state (Land) of Bavaria (Bayern). DB (German Railways) have a one day ticket for travel on local trains and buses within Bavaria called the "Bayern ticket". This is the best way to get to many places, for example Salzburg, "Price in 2nd class: EUR 25 plus EUR 6 per extra passenger (max. 4).", i.e. it costs you four €43 for an unlimited days travel in Bavaria.
This is a rail map of Bavaria showing all the lines it is valid on (bus routes it is valid on not shown - there are too many): https://www.bahn.de/p/view/mdb/pv/deutschland_erleben/allgemein/tickets/pdfs_laender-tickets/2015/mdb_190311_streckenkarte_bay_2015.pdf
Bottom centre you can see Garmisch-Partenkirchen and the train up Zugspitz.

Consider a daytrip to Herrenchiemsee, a palace replicated after Versailles on its own little island. Easily accessed by public transportation & my 2 teen girls thoroughly enjoyed their time there. We spent 3 nights in Salzburg. I highly recommend the Fraulein Maria bike tour. That was a highlight of our entire vacation. We opted for Mittenwald and the Karwendelbahn as an alternative to the Zugspitze. I personally felt it was a better choice financially and we enjoyed the small little town. Again we used trains for this daytrip from Munich as well.

You will be traveling in one of my favorite areas of the world! I will throw a few ideas at you. See if any sound interesting.

You will pass through Garmisch-Partenkirchen to reach the Zugspitze. If your family likes hiking, there is a wonderful gorge there called Partnachklamm. There is a small fee to enter. You can either hike through at the bottom of the gorge near the water or above the gorge (crossing the water a few times by bridge). I recommend walking/hiking in along the lower path and then hiking out on the upper path (there is a nice snack house with tasty homemade food on the upper path). The entrance to the gorge is a short walk from the Olympic Stadium used for the 1936 winter Olympics, which is kind of cool to see. The building where the Olympic stadium ticket counter is contains a really nice exhibition on the 1936 Olympics (virtually all in German; not of much interest if you cannot read German). There also is a Sommerrodelbahn (summer toboggan run) by the Olympic Stadium.

Hallstatt is most pleasant in the evening when the day trippers have left. Consider spending 2 nights there if you go. You could wander town the first afternoon/evening and then head to Dachstein in Salzkammergut on a full day there. It would add to your kids Alps experience. The ice caves are grand; they alone were worth the price of admission to Dachstein for me. There is also the Five Fingers viewing platform that looks out over Hallstätter See (Lake Hallstatt) there, along with good hiking. Hallstatt also has a salt mine tour.

I love Salzburg. It's great. There are all sorts of things to do there.

Berchtesgaden, near Salzburg is great, too. The area is known for the Kehlsteinhaus (Eagles Nest). Going there just for it is a little silly to me, but someone with an interest in WWII history will find the entire Obersalzberg complex (of which the Kehlsteinhaus is a small part) quite fascinating. I join Rick Steves in highly recommending Eagle's Nest Historical Tours, which does a 4-hour bus tour of Obersalzberg at 53 euro/person (35/euro up to age 14); since there are 4 of you, you might consider a private tour (250 euro for group of 4) if this sounds of interest to you. I did the 8-hour History Buff private tour, which I absolutely loved, but my travel companion found it a little overwhelming. Königssee is a nice lake surrounded by mountains that is near Berchtesgaden. The main entrance is quite touristy, but the lake gets very non-touristy at its far side (Salet Obersee stop on the boat), where there is an excellent hike around a small lake and through an Alpine meadow (past the cows who call the meadow home... watch your step!) to Röthbach Wasserfall (waterfall). There is also a salt mine tour near Berchtesgaden.

I guess you can tell I like to hike! :)

None of the hikes I mentioned are difficult.

Have fun on your trip!

We were in Germany and Austria last August and one of my favorite parts of the trip was our stay in Ramsau which is about a 20 minute bus ride from Berchtesgaden and in the national park. We also went to Hallstatt and while it was incredibly beautiful, it was crowded. We escaped the crowds only by going hiking in a huge thunderstorm! Ramsau was quiet and just about everyone there was German or Austrian. We went on some beautiful hikes that were accessible by public transportation. Think beautiful, high meadows with cows, sounds of cowbells and places to stop and get a bite to eat and a cold drink. Google "Ramsau, Germany" and you will see pictures of the iconic church which was next to the bus stop we used.

We used the bus to get to Ramsau from Salzburg, then backtracked to Salzburg by bus to take a train to Hallstatt. There is a shuttle service (eushuttle) that can get you from the Berchtesgaden area to Hallstatt in 90 minutes for 180 euro. For two of us, that seemed expensive and we wanted to take the train. For 4 people it might be cost effective to take a private car and save yourselves some time.

Have fun planning.

Thank you for all of these wonderful suggestions. My family loves to hike and be outdoors. We will be incorporating some of these great suggestions into our work-in-progress itinerary. Should lodging be booked as soon as possible?

I also stayed in Ramsau bei Berchtesgaden during my stay in the Berchtesgaden area. I will join Jennifer in highly recommending it. There are several nice hikes in the area. If the area is of interest to you, I would recommend the guide to Berchtesgaden written by David Harper. It has lots of good information, including very good information on hiking in the area.

I booked last year at this time for an August trip. Definitely got some good prices compared to rates I payed in the spring when I was booking for 2 adult children who decided to join us.

Thank you all for the wonderful suggestions. Some areas were not even on our radar until I posted this. We hope to begin narrowing down our list and trying to determine centrally located stays to minimize travel and allow for more time to take in the sights. I welcome any additional comments and hope to post a more specific schedule, open for comments and suggestions, soon.