I don't know how you are doing with your family search as I haven't heard back from you recently, but I have another piece in the puzzle for you. I found the death record for your granny's sister Betsy Mitchell, whom you have wondered about, which indicated she died in East Kilbride, Lanark, in 1998. I did this by entering her mother's maiden name "McGowan" in the Search of Statutory Deaths on ScotlandsPeople, and it gave me a result, as these names are entered in the Index after 1974. It appears that she was born around 1912. The entry in the Index than gave me her full maiden name, Elizabeth Clark Mitchell, and also her MARRIED name, which was Downie. I then was able to access her marriage, which took place 1931, in Blythswood District, Glasgow (which is in Central Glasgow). By doing this yourself you can have access to a lot of valuable information about your granny's sister!
Hugh