As promised, here is a chart to illustrate one possible way that my mother Florence, Elaine and Frieda are all connected.
There are a LOT of unknowns and assumptions here.
First, we are assuming that Joseph Brotman and Bessie Brot were first cousins, as family lore says. If so, then one of Joseph’s parents was a sibling to one of Bessie’s parents. On this chart, I am assuming that Joseph’s father Abraham was a sibling to Bessie’s mother Gittel Brot because I don’t think Abraham would have named a son Joseph if he had a living brother named Joseph.
Second, we are assuming based on DNA results that Joseph Brotman and Moses Brotman were brothers, making their children first cousins and their grandchildren, here Florence and Elaine, second cousins. The DNA results seem to support that assumption.
Third, we are assuming that Florence and Frieda are also second cousins based on the DNA results, meaning that Gussie Brotman and Sabina Brod were first cousins, meaning that one of Gussie’s parents and one of Sabina’s parents were siblings. Here, I am making the assumption that Bessie Brot, Gussie’s mother, was the sister of Sabina’s mother, but it could be that Bessie was Sabina’s father’s sister. I don’t know whether Brod was a name Sabina got from her mother or her father because in Galicia in those times, the state often treated Jewish children as illegitimate if their parents had only a Jewish marriage ceremony and thus assigned the mother’s name to the children instead of the father’s. So either is possible here.
So what does this all mean? Well, hold on because this is where it gets a bit slippery. Taking the above chart as true (which is still very speculative), it means that Elaine, Florence, and Frieda are all third cousins since they all have the same great-great-grandparents, i.e., whoever were the parents of Abraham Brotman and Gittel Brot. (I don’t know whether Brotman and Brot were two versions of the same name or two completely different names in the family; both exist as surnames so they could be as unrelated as someone named Rosen is to someone named Rosenberg, for example.)
BUT Elaine and Florence are also second cousins (as well as third cousins) since they are the children of first cousins (Louis and Gussie) and the grandchildren of siblings (Moses and Joseph Brotman). AND the same is true for Florence and Frieda: they are second cousins because they are the children of first cousins (Gussie and Sabina) and the grandchildren of siblings (Bessie and the parent of Sabina).
So my mother is a second cousin to both Elaine and Frieda (since her grandparents were first cousins), BUT Elaine and Frieda are not second cousins, only third cousins. Their grandparents (Moses Brotman and Sabina’s parent) were not first cousins, just second cousins.
That is consistent with the DNA results which showed my mother as a second cousin to Elaine and also to Frieda but showed Elaine and Frieda as likely third to fifth cousins.
I have no idea whether that is a help or not. In fact, I think I am more confused now than before. Please tell me if that makes no sense. Ask me questions. Test my thinking. Please.
And a big THANK YOU to my new cousin Phyllis for helping me sort through all of this!