I would be friendly with the woman but I wouldn't think of her as my mother. But she's calling her her real mother and her adoptive parents her parents. No, that's your birth mother. Your real mother is the woman that raised you. Not the woman that gave you up when you were two-years-old, for reasons they don't mention, and had something to do with two boyfriends. I would be extremely upset if the child I took into my home and raised was now calling her birth mother her "real" mother.