Train travel for Switzerland and Germany

A few thoughts.....

The trip from Ulm to Mürren will take the better part of a full day with, 4 - 8 changes. Be sure to specify Mürren BLM when you buy your tickets. The easiest trip appears to be a departure from Ulm at 08:04, arriving Mürren at 14:58 (time 6H:54M, 4 changes). It would help to know the exact date you'll be making that trip, as the details may vary.

There are two stations in Interlaken, and you'll need to disembark at the second one (Ost). One important point to mention. When you transfer to the Berner Oberlandbahn at Interlaken Ost, be sure to check the small digital display on the side of the coach you board, to ensure it's going to Lauterbrunnen. Some trains split at Zweilütschinen, with part going to Grindelwald.

Mürren to Schilthorn is an easy trip. The return adult fare is CHF 82.60 PP so one of the Swiss passes may save you some money (you'll have to crunch the numbers). I'm not sure if hiking down from the Schilthorn at that time of year is a good option? I'll let the others weigh in on that point.

Mürren to Lucerne is a very easy trip, about three hours with four changes. There are frequent departures from Mürren.

The trip from Lucerne to Freising is about six hours, with as few as two changes.

Given the travel times involved, you won't have much time to actually see much of the places you'll be visiting.

With a group of 10, are any children under 16, and related to other travelers on the trip, and what is the relationship?

In general, if the per person costs are 240 CHF or more, the Half Fare Card will save money. If not, then just buying tickets will be best. But my 1st paragraph may alter that advice. Look up prices at www.sbb.ch/en. Note that the first price you see assumes you have a HFC. These will be processed inside Switzerland and obviously don't apply to German portions.

In Switzerland, at least, with 10 people or more you should be able to get a "group rate". It's something like 10% off all fares, AND the 10th person is free. You should be able to Google the info or look on the www.SBB.ch/en website.

I'm quite sure you can't get group rate AND other discounts, but I'd certainly look into the group rate.
You do have to travel, as the name suggests, as a group to get the group rate. Germany may have something similar.

There are ten adults, five couples on this trip. Our intent is to leave in the mornings on the train trips with as few changes as we can as we will have our suitcases with us. I know it’s not much time but we wanted at least a chance to see some gorgeous mountains and villages by train on this trip. I didn’t know about the price on the SBB being only half the price, so I’ll have to look at those again. Our hotels are already booked so our schedule is to travel to Murren on Friday, October 26; to Lucerne from Murren on Sunday the 28th and then to Freising on Monday the 29th. On the trip to Murren, I’m thinking we might take a train from Ulm to Lindau that Friday morning after 9 and then catch train from there to Murren. What are your thoughts on that?

Spunchy,
10 people is a group. This means you can get special discounted group fares.
See here (DB): https://www.bahn.com/en/view/offers/germany/group-saver-fare.shtml
And here (SBB): https://www.sbb.ch/en/travelcards-and-tickets/tickets-for-switzerland/group-tickets.html

Changes are unavoidable, especially getting to Mürren. Access is via Interlaken Ost (change needed), then you need to change at Lauterbrunnen to a cable car, and back to a train at the top (Grütschalp). That's 3 changes minimum just to get into our out of the Valley. But after that there are fewer, Luzern is then direct from Interlaken.

When you go to board the cablecar up to Grutschalp, look to the right before you go up the escalators to the boarding area to see if there is a man accepting luggage and putting it into a large open cart for transport under the cablecar. The cart will then be attached to the train from Grutschalp to Mürren, and you pick up your luggage from the back of the little train once you get to Mürren. It makes the transfers much easier if you don't have to handle your luggage.

By late October the system may be so uncrowded they don't offer this service. Still, it is worth looking before you lug your bags up to the boarding area.