It's been over 20 years since I've been to Switzerland, but I traveled there with my 70-year-old mother, so...
I'd try to make at least one of the border-crossing train trips a fabulous one. The Centovalli run between Locarno, Switzerland, and Domodossala, Italy, is great (http://matadornetwork.com/trips/14-scenic-rail-routes-europe/) I don't think there's anything much in Domodossala, so you'd want to plan for only a short layover there. My mother and I loved this trip. Locarno is a big old resort city, attractive enough and situated on a lake, but not what I'd call charming.
The Bernina Express between Tirana, Italy, and St. Moritz/Chur, Switzerland, is highly touted but I've not taken that train myself. It's a priced-for-tourists train with special viewing cars. If you're interested in it, the Seat61 website explains how to book it relatively cheaply. It would be another fabulous way to move between Italy and Switzerland. Before paying full price for this or any other special train, be aware that weather in Switzerland can be iffy at any time of year. Heavy rain and fog can roll in, sharply curtailing your view of the scenery and making that $$$ train fare a painful proposition. The same caveat holds for the costly private (cog-wheel, etc.) trains up mountains.
There are many gorgeous train routes within Switzerland, too. The rail system is superior (though pricey on a per-mile basis), so you can see at least a couple different areas of the country in 3 or 4 days if you don't mind spending the time in transit. Typical connection times are just a few minutes, so it's easier to make day trips from a single city rather than moving from hotel to hotel every day or two, encumbered by luggage. If your stops are in smaller cities/towns, you may not need more than 3-4 hours in each one. Switzerland, for me, is mostly about the beautiful environs rather than specific tourist sites.
Try to fit in a Postbus ride up a mountain valley or across a high pass, unless one of you is prone to motion sickness. The buses are great, but those mountain roads are something else. The Val Verzasca bus out of Locarno is considered one of the nicest.
A boat ride on one of the lakes would add variety, too, if time permits. You don’t need a day-long or even half-day boat trip to get nice views.
It is extremely difficult to find an unattractive city/town (or an unclean hotel) in Switzerland, so where to go depends on terrain preference and how much time (and money) you are willing to spend on Swiss trains. I think a day in the mountains and a day on a lake would be a good combination, but the rolling dairy country around Appenzell is also nice.
Places I remember liking from earlier trips include the aforementioned Appenzell (pop. 6,000; be prepared to smell the cows, and this is about as far from Milan as you can go), Thun (pop. about 40,000, on the lake of the same name), Fribourg (historic town of similar size, on a hill), Murten/Morat (walled town also on a lake, pop. about 8,000). Gruyeres (cheese!) is a much smaller town near Fribourg, but I believe it's quite touristy.
If your mom has mobility or respiratory issues, check altitudes and terrain before committing to a destination. It's a warning sign if a place has no train service. That often means it's up in the mountains.
For ideas, I suggest checking out the destinations visited by the RS tours. I'm sure they are carefully selected. Since your primary destination is Italy, you may want to choose Swiss destinations outside the Ticino. That’s the Italian-speaking area, which includes Locarno, Lugano (my favorite), and Bellinzona (convenient RR junction with a castle). However, if you happen to hit bad weather, this might be the place to head. It tends to be sunnier than many other parts of Switzerland.