What are you going to do on Wed if it's raining? Same for Zugspitze take cable up/down.
You may be overly ambitious. Driving in EU is slow. 150 miles a day is fast pace. Grossglockner road takes about 4 hours one way, and its not close to Innsbruck.
Took me all day the last time I drove from Munich to Fussen. My sightseeing consisted of 4 churches on the way. Allow a minimum of 90 minutes to visit N-castle. More if it's busy.
2.5 hrs rt on the train to Zugspitz. One train an hour. Spend time sightseeing on the summit & it's an easy 4 hour jaunt.
don't drive in EU without Michelin maps & Green Guides (specifically designed for sightseeing by car).
Get the 1/200 000 scale map. It shows roads, scenic roads, sights to see (rated). I prefer the older Green Guides (ink drawings instead of photos) to the newer one with photos. Try eBay.
Everyone in your party must memorize the International Road signs.
On expressways, you must keep right except to pass. You wouldn't believe the road rage German drivers can express toward some jerk going slower than 100 mph in the left lane.
If you do drive into Austria from Germany, you must buy an Austrian road sticker at the first gas station across the border. Big fine if you don't.
Rental cars are way more expensive at the Munich airport than in town, but you will get lost trying to drive out of Munich. That's on reason why everybody needs to know the road signs. The driver needs all the help he can get all the time.
I think driving is the best way to see EU except for the big cities, but I'm not sure a beginner should tackle the Alps and you picked some of the toughest roads in the Alps.
Do not make advanced reservations at hotels when you are on the road. You will never time it right. Take your time & stop for the night when you get tired or it gets dark.
Assuming N-castle is a must, consider this: Munich to Garmish to Linderhof to Fussen for first night. Next day, see N castle, Wies Church and head toward Augsburg to pick up the German Romantic ROad. Michelin Green guide will lead you along it step by step. Side trip to Schwabisch Hall. If you have any time left, consult the Green Guide to see what else is in the vicinity
If N-Castle can be sacrificed, try an easier introduction to the Alps: Head for Salzburg if the weather is good keep going S from Salzburg on the A10 to 162 to Hallstadt with a stop at Gosausee on the way. arrive at Hallstadt from the south along the lake. Then Southe from Hallstadt to the Mighty Dachstein (cable car up toteh glacier & ice caves). Back on tehroadto Bad Ausee & it's series of cute little lakes to Bad Ischl to Salzburg via the Lake Ditrict, the Salzkammergut. If the weather is bad, stop in Salzburg for 1-2 days & pray for sun. If weather is still bad, it takes most of a day to visit Herrincheimsee.