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!