7 days in Germany in December!

https://www.bahn.com/en/view/index.shtml

Munich to Garmisch-Partenkirchen is an hour and 20 minutes by direct train. 22 Euros.

Munich to Nuremberg is a little over an hour by fast train and an hour and 45 minutes on the Regiobahn (regional/local train).

Munich to Berlin is only 5 hours by fast train, and goes directly from city center to city center (the Munich airport is significantly out of town).

Most of my initial confusion about German (and European) trains was that there are several stations in some cities - and you have to spell the city names correctly to get the right train selection. The RS guidebooks provide help on this, and Google maps can help too.

You should also explore the Deutsche Bahn website for deals.... And regional tickets that are good for multiple people.
https://www.bahn.de/en/view/trains/local-transport/regional-trains.shtml?dbkanal_007=L04_S02_D002_KIN0059_FLYOUT-ZUGFLOTTE-REGIOZUEGE_LZ01
https://www.bahn.de/en/view/offers/germany/christmas-markets.shtml?dbkanal_007=L04_S02_D002_KIN0059_AR1-Weihnachtsmarkt_LZ01

Note: There should be skiing on the glacier on the Zugspitze in Garmish-Partenkirchen at that time (you can rent skiis and boots at the top of the cog railway line.

Have great time!

20/12/19 23/12/19: Berlin (Munich to Berlin by flight.)

There are five fast ICE's per day that cover the distance in just under four hours. Your are a bit late but if you book asap you can get tickets for the 7:52 train (arr: 11.51) for €75.90.

The total cost for a cheap flight is more or less the same, and the travel time city to city is approx. four hours too. EasyJet and Eurowings fares for dec 21 start from €40 - plus approx. €17 for airport transfers plus luggage (approx €20-30 if you check a bag, more if you have to gate check your board case when it doesn't meet the rather strict specifications). But the train gives you four undisturbed hours, and you can avoid all that hassle with transfers and security checks.

No doubt the webmaster is going to yell at me again for being nasty, but you have one the worst proposed itineraries I have ever seen. You are going to Garmish on the edge of the most crowded, most expensive time of the year, and the weather will be dicey-- you can't see mountains in clouds.. As sights in EU go, Berlin and Munich are 3rd rate (4th rate for Germany). Nurnberg is OK, but nearby Passau & Regensburg are better.

It looks like you are already trapped into flying into Munich and out of Berlin, so consider this alternative: Munch to Passau--Regensburg-- Nurnberg (2-3 days) to the Romantic Road (Augsberg to Wurzburg)-- 2-3, then Berlin for no more than 2 days. 

It is perfectly fine to visit Garmisch in mid December. This is not the busy season as it is too early for good skiing (even on the glacier the skiing is so so this early but it is possible). Weather can be iffy any time of the year so don't let that stop you.

Munich and Berlin are great places to visit and a good contrast for the time that you have. I would also recommend one of the Motel One locations if that works for you.

To get around Bavaria, the Bayern Ticket should cover the three of you on days where you are traveling city to city, in Munich it also covers the local trams, trains and buses.

For Munich to Berlin I've done this by car, train and plane and my personal preference would be to fly from Munich to Berlin but only if I could find a cheap (less than 90€) flight, otherwise I'd opt for the train as a second choice.

As for the other poster's recommendation to visit 6 cities (not including Munich) in 9 days, well that is just doesn't make sense especially for one's first time to Germany so keep that in mind when considering their other advice.

DJ

Thank you everyone for the tips :)