Title; "Sins of the Father"
Author; indiefic
Summary;An AU set around the time of A New Hope. Padme didn't die. She's been living in exile for most of the twins' lives, but now it is time to return to Coruscant and the Emperor.
https://archiveofourown.org/works/4439918/chapters/10087058 Warning: Read at your own risk. This fic is no longer being updated. (I'm guessing that either the writer has moved on to other things, or RL no longer allows time for fic writing. )
It's a great AU. Some great smutty sex scences between Padme and Anakin/ Lord Vader. I do wish that there was a complete end to this fic, but....
The AU point for this fic, Padme doesn't go confront Anakin on Mustafar (with Kenobi stowing away), so Anakin never ends up in that suit. Lord Vader kills Palpatine, and becomes Emperor.
Leia and Luke have grown up knowing both parents, and spending time between Coruscant and Tatoonie.
If you don't mind unfinished fic,definitely give it a read.