If I was hired as a writer, Padme lived after ROTS. (Her death - the death of a strong woman and a leader - was done way too cheaply!)
Padme's parents knew she was still alive after the birth of the Empire. They identified the body of a dead handmaiden as their daughter. Padme used a body-double in the first 2 movies - Sabe and then Corde. Why not in ROTS?
Yoda knows. Obi-Wan does not. They feared Obi-Wan could reveal this ruse if he felt sympathy for his fallen apprentice in another confrontation with Vader, and that Darth Vader would pursue Padme relentlessly. At least this way, she could remain with one of her children - Leia. Also, with Obi-Wan NOT KNOWING, he wouldn't be very quick to refuse taking the infant Luke away, as Yoda needed him to do.
On Polis Masan, the birthing droids gave Padme a drug to simulate death, at Yoda's instruction. It fooled Obi-Wan and the droids were ordered to pronounce her dead. But Bail Organa knew, because he'd go on to hide Padme and fight a running battle against evil to protect her, even while serviing in the Imperial Senate as a presumed ally of Palpatine's.
Leia would be raised as an Organa so she could have a normal childhood and inherit Bail's seat in the Imperial Senate when she was older, so as to go on "making a difference" and oppose Palpatine when the time was right.
The charade becomes very dangerous and bounty hunters threaten to discover the truth. It costs Bail Organa the life of his wife, Breah, even. Darth Vader inadvertently does get involved and kills Padme afterall - this time by blowing up her ship - though he never knew his wife was a passenger - or even alive for that matter.
In the Expanded Universe, Leia remembers being raised by "aunts" after the death of her adopted mother (Breah). For a short time in her life, before Padme's true death, Leia might suspect that one of her aunts is actually her real mother.
"She was very beautiful, kind, but sad."
She remembers just feelings - images - like holos that R2D2 carries in his memory banks.
Defending Bail, Breah, Padme, and Leia, might be Ahsoka and Captain Rex.
Gee. I should be a writer. Oh wait....