I don’t think that Regina and Jefferson are related in any way because when she left Jefferson she told him he was right; never abandon family. She is also a master of redirection, basically using his initial feelings against him in a twisted manner. If you really loved your daughter you wouldn’t have left her in the first place.
Grace lost her Mother because of the Hatter’s work, he didn’t say she was dead. I wonder if that will play a part later?