>> I have not been to St. Moritz or that area, and I have wanted to see the traditional homes with sgraffiti in smaller towns.
As Slowpoke has also suggested, Guarda and Scuol would be the best places for that.
When catching the train to Guarda, if your train is travelling in the direction of Scuol, make sure you are in the front half of the train. When I went to Guarda, I was in the back half of the train, and the carriage I was in came to a stop beyond the end of the paved low-rise platform. I had a bigger step down, and stepped onto unpaved ground (see attached screenshot from Google satellite view). If you have mobility limitations, you'd want to avoid that.
A small bus from Guarda station will take you right up to the centre of the village, and the main street through the village from one end to the other is more or less level.
Photos attached to my trip report will show you both the beautiful sgraffito on the houses in Guarda, the size of the bus, the gradient of the lanes and the pavement surface. You could thoroughly enjoy Guarda with little difficulty, I would imagine.
Scuol Sot, the old part of Scuol near the River Inn, has a fairly level cobbled lane that goes through it, along which are several bus stops. You catch the town bus from Scuol-Tarasp railway station. For a level walk, get off at the stop called "Bügl Grond", and walk two stops to the stop called "Porta". There are more details about the bus, the bus stops and the timetable, in my trip report on Scuol.
The link to the Scuol town map in my trip report is now broken, but you can download PDF maps of Scuol and Guarda ("Ortspläne") from the following page:
www.engadin.com/servic e/informationen/ortspl aene/?R=1&S=2
Paper maps are also available in the Tourist Office (which is marked on the PDF map near the red-and-white number 39; the nearest bus stop is "Posta") and perhaps also the railway station.
Another beautiful area in Scuol is the small square called "La Plazzetta", in Scuol Sura, the upper part of town. The lane opposite the Belvédère Hotel in the street called "Stradun" provides the most direct access to La Plazzetta. It might be a bit steep for you, but it does have a handrail (see attached picture).
An alternative approach is along the lane called "Vi", which is less steep. The closest bus stop is "Bogn Engiadina". On the town map that you can download from the above link, the "Bogn Engiadina" bus stop is shown by a bus symbol near the red-and-white numbers 35 and 36.
From there, you would walk back to where the green-and-white numbers 11 and 14 are, turn left into that street (Via da l'Ospidal), then first left into "Vi". You are heading towards the blue-and-white number 82, which is La Plazzetta. There are also some lovely views of the mountains from Vi. My photos "La_Plazzetta" (11), (12) and (13) were taken from Vi (attached to my Scuol trip report).
>> Do you think I could do the bus trip to Soglio that you wrote about in a post? I could go up steps into the bus if there is a handrail, and my daughter could lift the folded walker. I would enjoy the scenery and walking some in Soglio.
Yes, I think you would be fine in Soglio. Buses are low-floor and have hand rails. It seems you have read my trip report, so are familiar with the gradient of the lanes in Soglio, and the paved surface. You do need to go up a hill to get into the village from the bus stop. I have attached photos below to give you some idea of the gradient.
>> For family gatherings, I have used only the cane to go into the homes or back yards. I'm just not as steady with the cane.
As you are taking a walker, that might be all you need, but it might be worth considering (in addition) a pair of extra-lightweight, collapsible hiking poles with (removable) rubber tips for added flexibility. Mine fit easily into the outer pocket of my suitcase for flights.
If you are taking a small backpack to carry your bits and pieces around during the day, look for one with loops on the outside to carry poles when they are not in use, such as this one:
assets.trailspace.com/ assets/8/0/2/3438594/D SC03264.jpg
With a set of hiking poles, you would really look the part, as every self-respecting man, woman, child and dog of whatever age in Switzerland would never be seen in public outside the city limits without their set of hiking poles! Well, I do exaggerate, but you will certainly see them everywhere, and they also seem to be favoured by older people instead of a walking stick.
However, hiking poles may not be a sensible option for you - only you can decide that :-)