In the original trilogy and followup history stuff, I always thought Vader fell long before the twins were born. I seem to recall Vader as a Hunter of Jedi. So, from my perception, Padme had went into hiding, and the Jedi were split up and hiding, as Darth Vader hunted down the last of them.
In the movies, the Clone Troopers (arranged and paid for by the Jedi, but loyal to the Emperor?) kill the Jedi. Vader kills some Jedi Babies (and I guess a couple real Jedi off-screen/ in holorecording).
Basically, Vader kind of sucked in Ep3.
So, Obi Wan having to be told by Yoda that "there is another" makes no real sense when he handed the kid over. Vader not knowing about the twins is reduced sense. (Leia was good at hiding her powers though!) Leia remembering her mother was just the drugs talking...
I wonder at what point Vader realized he had a son?