As I read it Lord Gregory has left Anne but without necessarily knowing she is pregnant.
Anne arrives with baby to announce lord Gregory is the father.
Mother sees her, pretends to be Lord Gregory and sends her away, presumably to protect her noble son from having to marry someone who may be beneath him.
He is frantic when he finds out his mother has sent Anne away no doubt to her death, because he loves her.

Compare this to Clyde's Water where Maggie's mother pulls the same stunt to get rid of Willie, with the same double-drowning result.