This sounds like a great trip but I wonder if you have adequately considered all the details, especially with respect to Appenzell and the Glacier Express to Zermatt. Some questions:
Have you made reservations at one of the Ebenalp guest houses? These mountain inns are very popular with the Swiss and you may find them booked up.
3 of the 4 guest houses listed on the Ebenalp website require some hiking to arrive. You won’t want to do this with your luggage, unless you are traveling with just lightweight backpacks. If not, you need to have a plan for your luggage while you are up on the mountain.
Have you looked carefully at the train and cablecar schedules to get you from Ebenalp to Chur? The named Glacier Express departs Chur at 11:06 am. Travel time from the Ebenalp train station to Chur is 2+ hours, depending on how many train changes you make along the way. There are 2 departures that will get you to Chur at 10:48, in time for the 11:06 GE: depart at 8 am for a journey of 2 hr. 48 minutes, with 2 changes, or depart at 8:30 am for a journey of 2 hours 18 minutes and 5! changes. The Ebenalp cablecar starts running at 7:30 and you should be on that one if you want to make that 8 am train. If you are staying at a guesthouse other than Ebenalp, you need to add the hiking time.
Here is a schematic map of the guesthouse locations and trails:
https://www.schaefler.ch/wandern/
The Glacier Express is a long journey—-6+ hours. You can do the same route faster by taking the local trains (you will have some changes on the way). Either way, added to the time for the journey from Ebenalp, it makes for a long day on trains. And expensive—-46 CHF for Ebenalp to Chur (not including the cablecar) and 88 CHF for Chur to Zermatt. You can reduce these costs with a Half Fare card or Swiss Pass—-have you looked at these?
You are going all the way to Zermatt to spend one day there and do one hike (the 5 lakes hike). We like Zermatt a lot—-it has lots of good hiking to offer, but you should be aware that your chances of seeing the Matterhorn on any given day are less than 50%. We did not visit Zermatt until our 4th trip to Switzerland, when we had time to spend 4 days/3 nights there. We did luck out and had glorious views of the Matterhorn on days 2, 3, and 4 (on our way out of town), but I suspect this is unusual. RS did not see the Mountain until his 3rd filming trip in Switzerland—-and then he put Zermatt a on his “good to see list”.
Without knowing whether you have considered all these details, I am going to suggest some changes in your trip. First, that you choose between Ebenalp and Zermatt—-including both makes for too much moving around and many hours on trains. Second, I will propose an itinerary that assumes you choose Zermatt, suggesting a logical route.
From your arrival at Zurich, proceed straight to Luzern for your first night. Spend 1-2 nights. From there, head over the Brunig Pass to the Berner Oberland. Choose Wengen or Muerren for your stay (we like both but lean towards Muerren as a base for hiking). Spend at least 4 nights there.
Then take the Golden Pass route (not necessarily a dedicated Golden Pass train) to Montreux. Spend 2 nights, perhaps in the smaller town of Vevey (closer to Chateau du Chillon).
Then to Zermatt, for 3 nights not just 2. Montreux to Zermatt is 2.5 hours by train, with one change (at Visp).
From Zermatt there are direct trains through the Lotschberg Basistunnel to Zurich taking 3.5 hours, usually with a single change at Visp (there is one with 0 changes). You could easily get to Zurich before noon, in good time for your 2 pm flight, although some might consider this risky (I would myself, anyplace else, but not in Switzerland). If you want to travel the previous day just to be safe, you stay most of the day in Zermatt and take an evening train to Zurich.
I have an alternate suggestion that includes Appenzell and will be back.
