I know what you mean. My Grandmother was a Henry, of the Patrick Henry line. Her mother was Jewish, so what does that make me? But then, Great Grandmother was also Welsh. This is all on my mother's side.
Family tradition on my fathers side has it that our branch of an old Scottish lowland family are descended from James 5 of Scotland.
Of course, James 5 was by-named The 'Gudeman o'Ballengeich', that is, the farmer of Ballengeich, which is a district of Stirling, just under the castle. James's fields were women, and his crops were bastard children. He had many, so it isn't such a big thing in Scotland to be descended from James 5.
Possibly Jewish. By Jewish law, Jewish lineage is derived from the mother.
You're saying this is your mother's side of the family. If your grandmother's mother is Jewish, that means your grandmother is Jewish. If her daughter (your mother) is Jewish, then guess what that makes you.