Help- feeling overwhelmed

For the Swiss travel portion: Forget Rome to Rio. Use the SBB website. You can purchase the half fare pass that will discount all of your train trips.

And for the routes within Germany, visit www.Bahn.de/en. You should buy these train tickets now: Munich to Fussen. ( for Neuschwanstein); Fussen to Munich ( 2 hours each way which is a long day). Munich to Stuttgart ( 2 hrs); Stuttgart to Basel, Switzerland (3hrs); After Basel you will be able to use the Half Fare Card for yourself and “ Half Fare TravelCards for Youth” for your adult children ( it’s valid for ages 16-25) to get discounts on the Swiss trains.

Basel to Zermatt takes about 3.5 hours; Zermatt to Lucerne 4 hours; and Lucerne to Zurich Flughafen ( the direct train to Zurich’s Airport) takes 70 minutes.
You don’t need to overnight in Zurich the night before your flight. I recommend staying in Lucerne because the trains are reliable and on schedule in Switzerland.
This might allow you to break up the 6-hour train trip from Stuttgart to Zermatt and overnight in Bern, Switzerland’s capital, which is 4 train hours from Stuttgart, The 2-hour train ride to from Bern to Zermatt can be done the following day.
All in all, you have a lot of time on trains with this itinerary.

You just need your passports.

I would use Omio or Trainline and forget about Rome 2Rio. With Omio and Trainline I think you pay a small commission but they are easy to use.

I think you're moving around too much and it seems like you're on a train everyday. With 8 days, I would stay in no more than 3 places and I wouldn't be taking day trips on trains (or buses) every day.

Yeah, I count about 4 days of time just being on a train. It takes a lot longer to get around because of the mountains and the time spent getting to and from the rail stations and waiting for trains.

The rail websites are pretty smart about routing you the most efficient way. Just put in departure and arrival stations, and approximate time of day and it will figure it out for you.

PS Luzern is only about 1.25 hours by train from the Zurich airport, so it's easy to spend that last night there instead of staying in Zurich.

For the final few miles to Zermatt, you will change trains in Tasch to a private train which costs about $10.

Wrong. You change trains in Visp and it takes you all the way to Zermatt. You only need to take the train at Taesch if you are driving a car, in which case you park it in the garage in Taesch and switch to the train to Zermatt for the last few miles.

It is 6 to 6 3/4 hours from Stuttgart with anywhere from 2 to 4 train changes. You might time it so you arrive just before your check-in time at your VRBO.

You can store luggage at Zermatt train station, right across the street from the Gornergratbahn station.
https://www.sbb.ch/en/travel-information/stations/find-station/station.1689.zermatt.html
Look at Luggage deposit or Luggage lockers.

It is 3 1/2 hours to Luzern. Think about taking a more scenic route by traveling via Interlaken and taking the Luzern-Interlaken Express to Luzern, Goes over the Bruenig Pass and is quite scenic. Takes an extra 50 minutes and an extra train change but worth it if it is a nice day.

Isn’t it called the Brunig Pass?

Technically, it is the Brünig Pass, but since I can't remember the secret keyboard code to type a "u" with an umlaut, I use the universal convention of adding an "e" after the umlauted vowel. In the German alphabet, "u" and "ü" are different letters.

Thank you all for the responses. We are re-thinking the stop in Stuttgart based on the train info and probably rearranging the trip.