We used to do trips as a couple & family in rented vehicles, following Rick's advice a lot, & finding our own back doors, but at age 71 (& 69 for my wife), I'd rather not drive in Europe any more. Most tours cover many places we've already been (especially those Rick likes best). BUT..... we never took a cogwheel train to a Swiss hiking area (that would be new for us & really fun). And we never went to Appenzell (is Rick's little cliff-side hotel still there?), but we did eat their cheese while staying at Walter's. And we never did Rick's favorite Dolomite hiking area in/on Alpe Di Suisi (but we hiked & loved the Dolomites elsewhere & we'd love to try new areas in the same mountains). Is there a "My Way" or guided trip which includes Appenzell, Alpe Di Suisi, and Swiss &/or other trains, by chance?
So - you want to see the Alps and Switzerland, but you don't want to drive? As experienced travelers, Switzerland on your own would be very easy to do, as the train system is so efficient and user- friendly. The country works so well, with much English spoken in the areas most visited. A car would be an impediment, with so many small pedestrian- only villages.
The RS My Way doesn't look like it will meet all your needs. We fell in love with all things Swiss on the RS 12 Day Tour, and have been back twice since. However, it seems you don't want that tour because the Dolomites aren't included?
I'm just trying to totally understand your question. Have you ruled out touring Switzerland on your own? It's quite a thrill, as you ascend on cogwheel trains, gondolas, chair lifts, revolving cable cars, open air cable cars, small gauge trains, etc.
Hope all things Swiss are in your future!
Here is the link to the description
https://www.ricksteves.com/tours/europe/my-way-alpine
Definitely look at the My Way Alpine tour.....it doesn't go to Appenzell but you could tack that on before or after the tour
If you are fit and experienced hikers and want to see the Dolomites at their best,, I highly recommend this small family-run company. They offer hiking every day, at two levels. , ://www.mountainhikingholidays.com/dolomites-hiking-tour-in-italy/
We are older than you but still fit and strong, and had a great time on this trip last Septembe.
You can do this independently and all by train.
Fly to Zurich and continue to Appenzell. (You might need to spend a night in Zurich.) Spend 2 or 3 nights in Appenzell. Is it worth it? Only you can say, so read up on things to do there.
Next go to Chur and take the Bernina Express to Tirano.
Editing as I posted before I finished my thoughts. [Slaps head]
From Tirano proceed to Milan and spend the night. From Milan, take the train to Bolzano and on by bus to wherever you wish to stay for Alpe di Siusi hiking. You can stay in Castelrotto but we like to stay in the AdS at AlpenHotel Panorama.
That covers your wish list. Lots of other good options in Switzerland or the Dolomites for enhancing your trip.
Did you ever decide on your itinerary? Have you taken he trip yet?