Well, it could be a very emotional encounter. Padme might see the great potential in Luke and Leia. She could be proud of them and the Jedi paths they might be on. Maybe she would have some advice for them about the Force and how to use it for good.
One possibility could be a time - travel plot. Maybe Padme somehow gets a glimpse into the future and meets Leia. They could bond over their shared experiences of being strong female leaders in a galaxy full of challenges. Padme might see in Leia the kind of woman she hoped her daughter would become, and Leia could gain wisdom from Padme's past experiences in the Senate and in the Clone Wars.
It could inspire hope. If the news of Padme meeting her children spreads across the galaxy, it would give the rebels more motivation. People would see that there are still connections between the past and the present, and that the fight against the Empire is not just a random struggle but part of a bigger story.
It could be that in this fanfiction, Padme is somehow brought back to life (through some unique plot device). She and Luke then team up to fight against a new threat in the galaxy. Luke would be in awe of her, having heard so much about her, and together they would use their combined strength and knowledge to protect the galaxy.
Perhaps Ahsoka and Luke meet while on a journey of self - discovery. Luke could be seeking more knowledge about the Jedi Order's past, and Ahsoka, with her experience of the Clone Wars and her connection to Anakin, could provide valuable insights. They might exchange stories and training techniques, which would be really interesting to see in the fanfiction.
Perhaps it's a time - travel scenario in the fanfiction. Luke and Leia, having discovered a way to travel back in time, meet their parents. Anakin would be shocked to see his grown - up children, and Padme would be in awe of the strong Jedi and princess they have become. They could exchange stories of their lives, with Luke and Leia learning about their parents' early days.
Well, one possibility could be that Leia is initially shocked and angry to meet Anakin. Since she knows he became Darth Vader. But then, as she realizes he's from the past and has a chance to change, she might try to guide him away from the dark side. They could team up against some common enemies in the different time period, like the Sith who are always plotting in the shadows.
One great storyline could be a 'what if' scenario where Anakin doesn't turn to the Dark Side. In this, he and Padme raise Luke and Leia together. The twins grow up with their father's Jedi training and the family lives in harmony, facing the challenges of the galaxy as a united front.
Their interaction would likely be filled with mutual respect. Padme, as a former queen and senator, would recognize Leia's leadership qualities immediately. Leia, in turn, would be in awe of Padme, knowing her story and her role in galactic history. They would probably exchange stories about their families, with Padme sharing memories of Anakin, and Leia talking about Luke and her adoptive parents.
A possible plot is a fanfic where Anakin, in his Darth Vader form, has a vision of a different future where he didn't lose Padme. This vision makes him question his loyalty to the dark side. Meanwhile, Luke and Leia are on a mission to rescue their father from the clutches of the Emperor. The story could be filled with emotional reunions and battles between the light and dark forces.
One possible plot could be that Anakin, Padme, Luke and Leia are sent back in time to the Clone Wars era. Anakin could have the chance to prevent his fall to the dark side, with Padme by his side to support him. Luke and Leia would be there to help their father, using the knowledge they have from the future. They could change the course of the war and save many lives, while also ensuring the Sith don't gain so much power.