"How did my mother die?"-

I don't think Luke was asking Leia if she REALLY remembered her mother, it was more a remark to break the news to Leia that they were twins. Remember Luke has seen everyone he has known as a boy killed - he lost his "Aunt" and "Uncle", murdered by the Empire on Tatooine; watched as Old Ben as he was cut down by Vader; see (hear) Biggs die at the Battle of Yavin. His quest is (initially) for revenge. (ANH).
Then he learns that Vader is his father (the person who killed Old Ben, probably ordered the deaths of his aunt/uncle, and partly responsible for Biggs' death). He doesn't know what to do. (ESB).
Finally, Yoda dies after telling him that, apart from Vader, he still has family alive within the Galaxy! Luke is not alone anymore and his quest begins again - not for revenge, but to restore his (living) family. So at the end of RotJ, luke is making the observation that Leia and he share the same parents, it is immaterial if she REALLY could remember her/their mother. He has redeemed his father and found his sister.