Anakin chokes Padme. . . he hurts her badly. She may die.
Obi-Wan defeats Vader and rushes Padme to a secluded place where she can get some treatment.
(according to the book) All her physical ailments are "repaired", but she has lost the will to live.
She has the babies, then dies.
(according to the book) Obi-Wan and Yoda conspire to hide the children and even have the foresight to make it look as though Padme's body is still pregnant for the funeral (Though, oddly, they don't think to change Luke's last name).
Padme still appears pregnant at her funeral.
So, the Emperor and Vader can see that Padme died. . . and every indication is that she died along with the child (Anakin didn't know about twins). The Emperor isn't necessarily lying to Vader. They can both see for themselves that Padme is dead. How are they to know that it wasn't Vader's actual crushing of her trachea that killed her?
Vader later learns about Luke's existence from spies after the battle of Yavin. He's putting up a poker-face with the Emperor in ESB during their conversation (because he was hoping to find him and turn him to the Dark Side *before* the Emperor was aware).
What's so freakin' screwy about that?
H