According to the OT, Leia remembered her mother a little bit. She said she didn't remember much more than feelings, but I still can't believe that she would have remembered her as a new-born. Even if you say it was because Leia felt her sorrow through the force it doesn't explain it. Luke would have been able to feel it too and he says he has no memory of his mother. The only practical explanation was that when the twins were split up, Luke was taken to Tatooine and Leia went with Padme and the Organas into hiding on Alderaan. Eventually something would cause Padme's death, but not before Leia had become a little girl and could have reason to have some memory of her mother.

The whole story of what happened to Padme would have made a great episode of the new TV series.