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.
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.
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.
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.
One idea could be a story where Padme's spirit somehow guides Leia throughout her life in the Rebellion. Leia could have visions of her mother's wisdom, which helps her make crucial decisions.
I really liked 'The Time - Traveling Skywalkers'. It's a story where all four characters are caught in a time - travel anomaly. They end up in different points in time relative to each other. Padme gets to see a future where her children have grown up strong despite all the hardships. Anakin has to face his past self and tries to guide him away from the dark side. Luke and Leia use their knowledge of the future to try and make the galaxy a better place in the past. It's a really engaging read.
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.
Here's another idea. Suppose there's a threat to the galaxy that can only be stopped by using a long - lost technique that Padme knew about. Luke and Leia, with the help of Anakin's spirit, embark on a quest to find out about this technique. They face many challenges, including political intrigue and dark side threats, all while coming to terms with their family's complex history.
There are some fanfictions where the time travel is not just about changing the past, but also about learning from it. For instance, Luke travels back to the time of his father's youth. Instead of trying to directly change Anakin's path, he tries to understand the root causes of his fall. He then takes this knowledge back to his own time to better prepare the Jedi order for future threats. And Leia, when she travels back, might focus on building alliances that could have prevented the rise of the Sith in the first place. This kind of plot adds depth to the characters and the overall Star Wars universe.
You could also explore their relationships in a post - apocalyptic Star Wars setting. Suppose there has been a great war that has changed the galaxy. Luke, Leia, Anakin (if redeemed) and Padme (if alive) have to come together and rebuild their family while also trying to restore order to the galaxy. Their relationships would be tested and strengthened in this new and difficult situation.