Itinerary & mode of transport

It makes sense to do the entire trip by train. But yes, it looks rushed. Very rushed. And don't underestimate the time it takes to go from A to B, Berner Oberland to Bacharach e.g. is not a short trip.

Vienna to Salzburg - Train, two options 1) oebb or 2) westbahn. Both have easy to find websites.
Salzburg to Munich - Train, see this website for the instructions - https://www.seat61.com/trains-and-routes/munich-to-salzburg-by-train.htm
Munich to Fuessen or Reutte - defer to others, but if you are going to see the castles, maybe take a group tour from Munich. Otherwise, it maybe makes sense to rent a car and drop it off when you reach Bacharach, but to be honest, it is all pretty crazy, kind of like Mad King Ludwig crazy.

Bacharach - I would probably fly from Frankfurt to AMS, but some might rather take the train.

Here's another way to look at things:

Day 1 - spend night in Vienna (travel day, will be jetlagged)
Day 2 - whole day in Vienna, spend night in Vienna
Day 3 - whole day in Vienna, spend night in Vienna
Day 4 - travel to Salzburg (2.5 hours in transit plus 2 hours changing hotels), spend night in Salzburg
Day 5 - whole day in Salzburg, spend night in Salzburg
Day 6 - travel to Munich (2 hours transit plus 2 hours changing hotels), spend night in Munich
Day 7 - whole day in Munich, spend night in Munich
Day 8 - travel to Fuessen (2 hours transit plus 2 hours changing hotels), spend night in Fuessen
Day 9 - travel to BO (8 hours in transit plus 2 hours changing hotels), spend night in BO
Day 10 - whole day in BO, spend night in BO
Day 11 - whole day in BO, spend night in BO
Day 12 - travel to Bacharach (8 hours in transit, plus 2 hours changing hotels), spend night in Bacharach
Day 13 - whole day in Bacharach, spend night in Bacharach
Day 14 - travel to AMS (6 hours in transit, plus 2 hours changing hotels), spend night in AMS
Day 15 - whole day in AMS, spend night in AMS
Day 16 - whole day in AMS, spend night in AMS
Day 17 - leave AMS

Overall, this doesn't sound very fun at all to me.

What if we flew into Zurich and gave up Bacharach? One night in Zurich then do Berner Oberland, then Munich/Fussen, Salzburg, Vienna. It seems there would be just one long train/ car travel day getting out of Switzerland. When I look at Rome2rio site, why does it seem like train takes a lot longer than driving?

What if we flew into Zurich and gave up Bacharach?

If you give up Amsterdam as well that would be a much better itinerary.

It seems there would be just one long train/ car travel day getting
out of Switzerland. When I look at Rome2rio site, why does it seem
like train takes a lot longer than driving?

From where to where?

which train or trains is/are so slow that a car can beat it/them?

Rome2Rio is an algorithm which is often wrong. General idea about solutions but then you need to put real data into a timetable like the DB (who operate and supervise the trains in Germany and who are highly reliable all over Europe) website or app (for research I find the website more productive on a laptop) and look at the day and time you are interested in. You may have given Rome2Rio the idea you wanted to travel in the middle of the night, or needed a long layover.

Let us know where the problem is and we can often find you a better answer. Or tell you that there isn't one.

I’m looking at Interlaken to Munich or Fussen. What would be the fastest way/route to travel? Is it true that cost of a rental car if pick up and drop off are in two different countries is prohibitively expensive compared to train even if there are 4 adults traveling? Thank you for your help.

yes it will cost you a fortune to drop a Swiss car in Germany.

Depending on the route you drive it will take you five and a half hours to six hours to drive to Munich. Plus at least one rest stop and probably a lunch stop, Plus traffic plus accidents/breakdown which create more traffic, plus if you drive on the Austrian highways you will need an Austrian Vignette. Plus because your car is Swiss you won't have a German Umweltplakette on the windscreen so won't be able to enter the Munich environmental district.

Trains to Munich Hbf from Interlaken Ost can be as fast as 5:34 with quick and easy changes in Spiez, Bern and Zurich, or half an hour faster with just a change in Zurich.

I don't see that the train is at all slower to Munich.

I got a headache reading Emily's breakdown of your itinerary, and probably won't be able to sleep tonight. What Badger said about dropping Amsterdam, what Nigel said about car rentals in Switzerland (as expensive as it gets even without any drop-off fees). Stick to the lower end of Germany and parts of Austria, more than enough for two weeks. If you can, save the BO and Amsterdam for another trip.

Fly into Vienna- 3 nights
Salzburg 2
Munich 2
Fussen or Reutte 1
Bernese Oberland 3
Bacharach 2
Amsterdam 3

I did Interlaken to Fussen and one of my connections was 6 minutes, it was ridiculous I only made it because I ran and used my luggage to keep the doors from closing. Have you thought about day tripping to Salzburg from Munich instead of switching rooms? I've been to everywhere you listed except Vienna and Bacharach. Bernese Oberland is nicest place on your list so don't count anything from there. Amsterdam is nice but super small, make sure to get reservation to Anne Frank it sells out like yesterday. You could probably cut a day from Amsterdam and still get the main vibes.

I would drop Amsterdam from your itinerary. Or Vienna if you are stuck on Amsterdam. I'm not really a big fan of Munich and seeing Neuschwanstein (It's really not that old or authentic and you only get to see a small portion of it).

If it were me I would either do Vienna, Salzburg, Bernese Oberland, Rothenburg ob der Tauber and Bacharach or
Vienna, Salzburg, Bernese Oberland, Rothenburg, Bacharach and Amsterdam.

If you want another place in Switzerland, you might want to check out Luzern.

Either of my suggested itineraries will work well by train. Unlike many of the people on this website, I am usually ready to move on from a location after a couple of nights. I know people insist you must stay in a location for 1 week, 2 weeks, 1 month, etc., but I get bored and would rather move on.