Luke: Leia... do you remember your mother? Your real mother?Leia: Just a little bit. She died when I was very young.Luke: What do you remember?Leia: Just... Images, really. Feelings.Luke: Tell me.Leia: She was very beautiful. Kind... but sad. Why are you asking me this?Luke: I have no memory of my mother. I never knew her.
George Lucas: "The part that I never really developed is the death of Luke and Leia's mother. I had a backstory for her in earlier drafts, but it basically didn't survive. When I got to Jedi, I wanted one of the kids to have some kind of memory of her because she will be a key figure in the new episodes I'm writing. But I really debated on whether or not Leia should remember her."
Star Wars - The Annotated Screenplays, page 291
So George Lucas was really conflicted about whether or not Leia should remember her mother, but as we know the decision was that Luke never did know her and that Leia had vague memories from when she was very young. And as we also know this is not the story of the prequels.
I don't know... it just feels off to have vague memories from when you are just minutes old. Certainly that your mother was kind but sad. And why didn't Luke remember anything? Is there a special mother daughter relationship going on here?
The story should of course be that the twins were separated. Luke was given to the care of his uncle and aunt, while Leia went with her mother to Alderaan. And she dies at least three years after the birth of the twins, and not in childbirth as told in the prequels. Whether or not this death happens in the remade prequels is a matter of consideration when rewriting the story.