traveling from Munich to Geneva and back

This plan is do-able. You have 2-3 night stops, which is good.
I too would have said do this all by train, though I admit Munich to Zurich is a long haul by a not particularly fast train. But, if you have already planned to rent a car, then you have already made the decision how to get around.
Are you aware that the cities you list, you cannot drive from place to place in the city centre. You will need to ask each hotel if they have parking (and for how much), do not assume hotels have parking. At the very least, do not pick up your car until you leave Munich, airport to city centre is easy and fast by train.

Look up all your routes on https://www.viamichelin.com/ This will give you routes, distances times and costs. Time assume no stopping, so add at least 25%. For Switzerland you will need an Autobahn Vignette (Toll sticker, CHF 40). A German hire car will almost certainly not have one. You can buy it at the border.

I would skip Zürich, go straight to Luzern. You wouldn't be able to drive into Zürich anyway, it would be "park-and-ride". If you want a nice place to stop between Munich and Luzern, I recommend Lindau. But you will have little time, as that is a full day's travel.

You also cannot drive into Geneva without expensive (and non-central) parking. Best just get a train from Montreux.

According to Viamichelin, Montreux to Salzburg is 7½ hours driving (plus stops), via Munich! Or 9h10 on the scenic route via Innsbruck. You could add time in Innsbruck en route.

I don't think driving will be much, if any, faster than the train on these routes. There are train routings that require less than 8-1/2 hours between Montreux and Salzburg.

Within Switzerland, having a car won't add much flexibility from a time standpoint because the Swiss trains run so frequently. They're also utterly reliable. But it appears that the train trip from Montreux to Salzburg is a very costly one (I didn't price out the others). Perhaps a Swiss half-fare card would be worthwhile?

I assume there's beautiful scenery all along your route. Will the driver be able to enjoy it with his/her eyes on the road?

Thank you so much for your input. If we decide to cancel our rental car, what would be the best rail pass or train ticket pass? The Eurail global pass is very expensive!

Hello again kdorst4, "best rail pass or train ticket pass" - probably neither, just normal tickets.
Read this: http://seat61.com/Railpass-and-Eurail-pass-guide.htm
A Swiss Rail pass may be the best option for in Switzerland, as you are spending a lot of time there and you will probably want to go up some mountains while you are in Luzern. For Switzerland, there are 3 options:
1) Pay full fare for all tickets.
2) Buy a half fare card (CHF 120 for one month, click here), and pay 50% for all trips in Switzerland.
3) Buy a Swiss pass.
Sorry, you will have to do the arithmetic yourself and decide. You can look up fares on the Swiss Railways site: http://www.sbb.ch/en/home.html

For the other trips (Munich - Swiss border, Swiss border - Salzburg and Salzburg - Munich) advance purchase will get you the cheapest tickets. See the German Railways site: https://www.bahn.de/p_en/view/index.shtml and the Austrian Railways site: http://www.oebb.at/en
Munich airport - Munich HB (central station) is a local ticket, no discount for advance purchase.

Don't get a Eurail Pass.
To save money, buy nonrefundable tickets well in advance to get the best price.
Munich to Zurich may be best done on a bus, which is more frequent, faster, and less money (when bought in advance) and, from what I heard recently, has great wi-fi.
Montreux to Salzburg can be done in 8 1/2 hours or so with connections in Lausanne and Zurich. Full fare for 2 would be 356 CHF, but you could get advance nonrefundable tickets for 150 CHF. If you did get Half fare cards, the full fare price would be 214 CHF, but the nonrefundable price does not change. So with Half fare cards, you could still maintain flexibility without spending too much more.

thanks for all of your replies! one more (but probably not really the last...) - we have plans to stay in Montreux for 3 nights, but do little trips to Lausanne and Geneva. Is Lausanne a better place to stay than Montreux?

Better? Depends on what you want. Lausanne is more a city, Montreux is more a resort town. Lausanne is more central for transportation.

This may or may not work with your plans but since the countries are so close, it's quite easy to fly. I just checked Swiss Air to Geneva from Munich and the round trip is $137.00 using dates next week. The flight is just over an hour and it's non-stop. This saves quite a lot of time over trains from Germany. Once in Switzerland, you can go almost anywhere by train, bus or boat. I did not check flying into Zurich but that may work better with your plans. There are trains at the airports here which will take you where you want to go. When you visit the Geneva/Montreux area, if you want charm combined with ease, I would stay in Vevey over Montreux or Lausanne.