Help my in-laws plan their trip!

They will be in Rome for the heat of the summer, and the Jubilee, which is expected to bring an additional 10 million folks to Rome. This might not be the best year to be a first - timer in Rome.
Murren and Scotland should have wonderful summer weather, however. It does rain in Scotland, so be prepared. These three places would require a range of clothes, from the heat of Rome to the Alps.
They will also be losing significant time traveling, as the three areas aren't close together. Can they add a few days?
Murren lodging will book up quickly for June.
Any chance of their closing three places closer together?
Kudos for helping out!

Often, first time visitors planning a trip to Europe underestimate the time and distance in trying to cover so much of Europe in a very short amount of time. The really should consider eliminating at minimum one of those choices. With the current itinerary, they've lost days just for travel between locations. With walking mobility issues and Rome's heat and Jubilee, I'd consider eliminating this one.

Let's hold optimistic that this isn't their one and only opportunity.

Have they identified what it is they want to see/do at each stop.

At this point they have 2 full days in Murren and Rome and 3 days in Scotland. June 23 and 26 are travel days and little else will happen.

If what they want to do at each stop can be done in the available time, good for them. I would not want to spread myself that thin.

Walking mobility is somewhat limited

Care to share some additional details? Offering 'guidance' is easier when the situation is well defined.

It’s understandable that they feel this might be their only chance and have bucket list items they really want to see. If that’s the case, is there any possible way they can add on some days? Trying to cover these places that are so spread out in 10 days is going to leave them exhausted and feeling like all they did was travel from place to place. Each time they move it takes away a full day. Do they realize it takes 8.5-9 hours with lots of train changes with luggage to get from Mürren to Rome? If you say their mobility is a bit limited that sounds like an issue to me. All around, I really think they either need to add on time to this trip or simplify where they are going to be realistic about mobility and travel logistics.

If they can add on some days to make it 2 weeks, they could do something like:
Fly into Rome - stay 3 nights
Rome > Luzern - 2 Nights
Luzern > Murren - 4 Nights
Murren > Zürich Airport to fly to Scotland (make sure it’s an afternoon/evening flight)
Scotland - 4 nights

If they can absolutely only do 10 days and insist on all 3 countries, I think they need to switch Mürren to Luzern, as they can get to Luzern with only 1 train change and going from Rome to Mürren is just too much in one day for limited mobility.

Alternatively you could try to share with them how memorable it could be to really soak all 10 days in one region and actually see more - 10 days in UK/Scotland or 10 days in Switzerland & Italy would give them a lot of European experience. All 3 places they want just need 2 weeks minimum to even consider.

If you in-laws are retired, I'm assuming, please convince them to travel spring or fall, not in the summer heat and crowds.
I like wanderweg's itinerary, but I'd reverse the order. For first-timers, start in an English-speaking area, and end in Rome. Rome is hectic and chaotic, and would be better once the folks have adjusted more to international travel.
Again, kudos for helping them!

Simple advice - get a travel agent! That is what they do for a living, especially for first timers. I put up a post a few weeks ago about them.

You've also limited yourself by posting in the Swiss forum. And they're trying to accomplish way too much.

A travel agent isn't always the best option. Too often I've seen travel agent recommended itineraries that are bonkers. Unless you get an agent who specializes in these areas specifically, I wouldn't recommend that advise at all.

I don't have nearly the experience of others on this forum. Just one comment on the mobility issue.

I love European trains. They are very well organized. Often they are faster and cheaper than flying. However with mobility issues planes might be a better choice. If your in-laws have anything larger than carry-on suitcases they may have trouble getting them on and off the trains. It can be hectic to figure out the best place to board and there are generally several steps to get up and into the carriage. Planes won't save you time or money, but they might be less stressful in this particular case.

If you haven't found it yet, this website is very helpful for understanding train travel in Europe. You don't have to use them for booking , but useful for planning. https://www.seat61.com/

Happy travels for your family!

Great advice above about extending the length of the trip to better accommodate the bucket list. I have a cautionary tale that might convince them to slow it down or limit the itinerary.

A couple of years ago, newly retired dear friends of ours decided to finally take that dream trip: she wanted to go to Scotland due to ancestry and an uncle she had seldom met, while he wanted to go to Switzerland as he had long envied our visits there. And while they were in Europe anyway, he insisted they had to go to Stockholm to see his beloved nephew, whom he had not seen in many years. They had 2 weeks total. Day one in Scotland, they woke up sick in Inverness, with Covid. After one day to rest and another day in which they managed a short visit with the family there despite the illness, they flew to Zurich on a hideous itinerary and arrived extremely late at night, spending the next day not touring but recovering once again. Day 5 of the trip they traveled to Lauterbrunnen where we had insisted they spend 5 nights or skip it. This segment of the trip was great and although they were still a bit tired, they had a wonderful intro to Switzerland and got fully rested. At this point, they were about 10 nights into the trip and have to get to Stockholm which involved a night in Paris (crazy flight planning). Four nights in Stockholm and they flew back to the West Coast, again exhausted. A few weeks later they acknowledged they didn’t realize how impractical the itinerary was, that they would not try anything like that again but allow more time since they have it now, and take note of geographic proximity. These are not inexperienced travelers as one of them hails from Lebanon and they have made stops in Europe before: a few nights in Paris traveling to and from Lebanon, business trips for him to several international locations, and a 10 day Italian “tour” under our wings when we lived there. But common sense did not factor into planning this trip as they were afraid they’d not go back again, at least for a long long time.

Something we have learned about ourselves in retirement travel is that bad transfers exhaust us. We will pay more for a flight is the schedule is better and there is no need to change planes AND we can arrive in daylight.