It would also be useful for you to visit the Wanlockhead Mining Museum (the next village) open Wednesday to Sunday 11am to 3pm.
So if the hotel could shuttle you there (or use the 30/31 bus), you could visit the Museum, then catch the bus down to Sanquhar, visit the Toll Booth Museum at Sanquhar (free, a very interesting place) then train to Glasgow. That way you have got the most possible benefit from your trip "home", understood as much as you can about their life up there.
It would be nice for you to use the Leadhills Wanlockhead Railway (the miners railway) but they open on Sunday only, so that might be asking too much.
In Summary from Edinburgh, if you catch the 0925 bus you get to Leadhills at 1249 after a 1 hour 18 minute connection at Abington services- time for lunch: or leave EDI at 1320, arrive Leadhills at 1522 after a 6 minute connection. I have recent experience on that bus route and think that is excessively tight. So use the morning bus.
Then to Sanquhar the 0910 bus to Wanlockhead, then the 1146 or 1416 to Sanquhar for the Museum, then there are trains at 1319, 1519 or 1719 to Glasgow, just buy at the machine at the station or on the train, no advance fares.
Hope this is all helpful. A bit of thought has gone into this, from someone who knows the area and how connections work. I like a challenge.
At Leadhills the bus stops at the Hopetoun Arms.