Becky,
Whereabouts was she born, do you know? Did she live all her life somewhere in Dumfriesshire? Do you know any other aunts, uncles, cousins on that side at all? All small clues help.
So your Nana's mother was Elizabeth Stewart and she was a single mother in 1915, so her child (your Nana) was raised by Elizabeth's brother and his wife. is that right? Just confirming.
My grandmother was also born to a single mother, also named Elizabeth, but in 1908 in Argyll. My grandmother was raised by her mother's parents. My grandmother, in turn had her own baby while single (my Mum) and that baby was raised by an aunt and uncle, Elizabeth's sister and her husband. I know it can be a difficult thing to research due to the secrecy resulting from the scandal of the so called "illegitimate" birth at the time. My Mum is 87 and still hates to talk about any of it all!
Mary