Hello Heather
Welcome to MySwissAlps
I have worked out three possible routes for you and your elderly father to travel from Zermatt to Murren.
I am of your father’s generation, and I am a lifelong enthusiast for public transport. (My dad was a bus driver, and we lived within sight of the London to Edinburgh main line railway.) I would unhesitatingly vote for route number two.
Route One Glacier Express( https://www.myswissalps.com/activity/glacier-express/) via Andermatt
Take the 08 52 Glacier Express to Andermatt, arrive there at 11 46. There is a tight across the platform connection to the 11 50 down to Gőschenen arrive 12 06.
At Gőschenen you walk past the station building (no bridge or subway) and get the 12 09 heading for Zurich. Get off this train at Arth-Goldau at 13 07.
At this station you walk past the station building (no bridge or subway) and catch the 13 15 to Luzern arrive 13 41. You do now get some respite.
Get the 14 06 Luzern-Interlaken Express to Interlaken Ost arrive 15 54.
Get the 16 04 train to Lauterbrunnen, making sure that you are at the front of the train in a carriage marked as going to Lauterbrunnen.
Walk under the road to the cable car going up to Grűtschalp, and from there take the little train to Műrren, arrive 16 54.
Advantages You get a lot of good scenery, but nothing I would call outstanding.
Your dad will be able to boast he has been on the Glacier Express.
Disadvantages
A 8 hours travel, with just one break of 25 minutes
B Each passenger will have to pay a reservation fee of forty-nine Swiss Franks.
C SEVEN changes, two of them ‘tight’. If you missed one of the connections, the journey will become nine hours.
Route Two Gently Does it via Kandersteg (https://www.myswissalps.com/activity/lotschberg-mountain-railway/)
Get the 08 06 local train from Zermatt to BRIG, arrive at 09 32. Do not try and catch the 09 36 departure. Go in the nice Patisserie near the booking office and have ‘Brunch’.
Get the 10 36 RE1 train to Bern via KANDERSTEG. Sit on the left for absolutely outstanding views over the Rhone Valley. Get off at SPIEZ at 11 44 Get the 12 06 RE9 train to Interlaken OST arrive 12 26
Get the 12 34 train to Lauterbrunnen, making sure that you are at the front of the train in a carriage marked as going to Lauterbrunnen.
Walk under the road to the cable car going up to Grűtschalp, and from there take the little train to Műrren, arrive 13 24.
Advantages
a A relaxed journey with one long break and one medium break.
b an acceptable overall journey of 5 hours and 18 minutes
c no tight connections
d the first 15 minutes out of Brig are fantastic.
Disadvantages None
Route Three Short but definitely not Sweet
Get the 08 06 local train from Zermatt getting off at VISP at 09 19.
Get 09 27 EC train bound for Basel, get off at Spiez at 09 53. This train will go through the Lőtschberg BASE tunnel.
Get the 10 06 RE9 to Interlaken Ost, arrive 10 26
Get the 10 34 train to Lauterbrunnen, making sure that you are at the front of the train in a carriage marked as going to Lauterbrunnen.
Walk under the road to the cable car going up to Grűtschalp, and from there take the little train to Műrren, arrive 11 24.
Advantage Speed. Exactly two hours quicker than Route Two.
Disadvantage. Base tunnel without scenery.
Very best wishes for your detailed planning.
Roger