Catherine Vance is my mother's mother's mother's mother's mother's mother's mother. That means I and my mother has the same mitochondrial DNA that Catherine had. My mother's mitochondrial DNA has been tested with Family Tree DNA and she has an exact match with a man whose parents were from Scotland. Based on this finding I think it is likely that Catherine's maternal line was probably Scots-Irish, a common ethnicity in Western Pennsylvania at the time.
There are several strategies in which we could use these mitochondrial DNA results to test theories on Catherine's parentage.
1. We could track Margaret (Vance) Shaw's mitochondrial descendants and ask one of them to be tested.
2. We could track the mitochondrial descendants of the sisters of the wives of other Vance men in the area who were old enough to be Catherine's father.