Here is a possible change to ANH and ROTJ which will probably win me no friends.

For me one of the flaws of the OT is the near lack of a mention of Luke and Leia's mum.

She would become a key, if disappointing figure in the PT but the OT skirts over her almost entirely.

What if Padme didn't die in ROTS and is still alive all the way up to ANH where she is destroyed with Alderaan?

The message could be altered so it comes from her mother and not her stepfather (Padme had more time with Obi-Wan than Bail did and she went to Tatooine) so telling Leia to go there in a time of trouble makes sense.

Padme may not know Vader is her husband or Vader knowing who she is protects her because bumping off a former senator and mother of a current one would raise questions Vader doesn't want asking.

He could even know Leia is his daughter which would explain the lack of results the Dark Lord seems to be getting out of interrogating her.

Come ROTJ you would then just have to edit out the line about her dying when Leia was young.