So in Clone Wars we learn that Anakin never wipes R2's memories. It's entirely probable that he eventually does after the almost-fiasco of having all their intelligence and battle strategies fall into the Separatist hands. Also, R2 doesn’t seem to recognise Obi-Wan in ANH (Ep 4).
BUT! What if R2's memory was never wiped? So he still has all the memories of Anakin and Padme he had when they were young and in love. And the twins get to learn about their parents and the people around them by watching home holovids.
Bonus: Anakin got into the habit of talking to R2 and R2 recorded it. So they have a kind of running diary of the good man their father was and how the war and Palpatine changed him.
Family pictures - Luke and Leia explore R2's memory banks
BUT! What if R2's memory was never wiped? So he still has all the memories of Anakin and Padme he had when they were young and in love. And the twins get to learn about their parents and the people around them by watching home holovids.
Bonus: Anakin got into the habit of talking to R2 and R2 recorded it. So they have a kind of running diary of the good man their father was and how the war and Palpatine changed him.