actually, that really has nothing to do with leia's memory of her mom, i was just throwing that out there.
however, while I hesitantly except the Force connection view coupled with a Mother/Daughter connection thing going on, never was it even hinted that Padme was connected to the force, so since she only lived all of 5 minutes (if that) after giving birth to Leia, what causes the connection/memories. For Luke's connection with his dad, his dad is still alive, and he didnt notice it until after being told Vader was his father. So unless leia had some contact with her mom whats causing it, because like i said, it wasnt the umbilical cord...well that and the comment is phrased in such a way that it seems Padme survived for at least a few months after giving birth.
-Darth Simon