Why can't she simply say: "That guy I interviewed was your father, small world huh!"
It wouldn't hurt their relationship at all, and wouldn't make it look like she's keeping terrible secrets. Why does she need to keep this secret from her GF? It's a separate matter from investigating them mother.
Also - people think the father is dating a student, the Daughter thinks her girlfriend is leaving her for a man, I get the feeling that we're going to be misled to believe that the mother had an affair too.