Has Leia 'forgiven' Anakin Skywalker for his crimes as Vader? Yes, in the “Legends” part, she even named her third child for him, as a symbol of his heritage and redemption. However, it's more than acceptance that Anakin is her BIOLOGICAL father and she got her personality and Force sensitivity from him.
Darth Vader didn't learn he had a daughter until Return of the Jedi, when he stood before Emperor Palpatine. The Emperor's power probed Luke's mind, attempting to goad him to fall to the dark side, and he discovered Leia's existence. "Sister," the Emperor taunted.
However, Leia's strong-mindedness during Vader's probe denied him the opportunity to discover she was his daughter. That serves to justify Vader's lack of awareness of his connection to Leia, although, perhaps, not as satisfyingly as if Lucas had planned for the relationship from the beginning.
Star Wars is finally exploring Leia's emotional reaction to the revelation Darth Vader was really her father - as her identity is transformed. Star Wars has finally revealed Princess Leia's reaction to learning Darth Vader was her father. Return of the Jedi was one of the defining moments in Leia Organa's life.
Vader doesn't know he has children in 'A New Hope. ' When Vader and Leia interact in A New Hope, Vader doesn't yet know he is her father. In fact, at this point in the story, Vader doesn't even know his children are alive at all.
No evidence would suggest that Darth Vader knew that Leia Organa was his daughter the entire time. However, in the final battle with Luke Skywalker, he learned that Luke had a sister. But the important part is that it was never shown that Vader found out that this sister was Leia.
After the Battle of Endor, Leia trained as a Jedi with Luke, but left the Jedi path after sensing it would result in the death of her son.
In the post-2014 canon universe, the story that reveals Darth Vader discovering Luke Skywalker's identity (and thus the fact that the Death Star's destroyer is his son) is issue 6 of 2015's Star Wars comics by Marvel, which takes place sometime shortly after A New Hope.
Leia Organa-Skywalker
Leia Amidala Skywalker (portrayed by Carrie Fisher) is the wife of Han Solo, the mother of Ben Solo, the younger twin sister of Luke Skywalker, the daughter of Anakin Skywalker and Padmé Amidala, and the granddaughter of Shmi Skywalker, raised by Bail and Breha Organa of Alderaan.
This is not because the Third Sister knows that Leia is Anakin Skywalker's child; it is because the Third Sister found a link between Obi-Wan and Bail Organa and she believed Obi-Wan would do anything to save Bail's daughter.
However, she chose not to tell Anakin, presumably because he was about to go into a battle. Anakin was prone to letting his emotions affect him, and knowing that Padme was pregnant would've thrown him completely off the task. And Padme probably didn't think that her husband would be fighting battles for months to come.
It is unclear whether Yoda would be more or less forgiving than Obi-Wan but one thing is certain - the former Grand Master would be ready to treat Anakin as an ally, following the events on the second Death Star. In Star Wars: Revenge of the Sith (2005), Yoda never really lost faith in Anakin in the way Obi-Wan did.
In Star Wars Legends Leia was visited by the force ghost of her father Anakin Skywalker, the man who used to be Darth Vader. It wasn't a pleasant meeting as Leia was unable to forgive him for the things he'd done no matter how hard he begged, and it was the only time she saw him.
Affiliation. After discovering she was Force-sensitive, Leia Organa Solo utilized several lightsabers through her career as a Jedi of the New Jedi Order.
Yoda. Yoda's knowledge of Luke Skywalker's true parentage was also confirmed in Return of the Jedi. As with Obi-Wan, Yoda believed that Anakin's fall to the dark side made him unsalvageable, with the Darth Vader persona being his only identity following his ascension to Sith Lordship.
Vader found out before Palpatine
This was seen in the scene between Darth Vader and Emperor Palpatine, wherein the latter told his apprentice during the earlier part of 'Star Wars Episode V: The Empire Strike Back' that Luke was Anakin's son.
He was thinking to himself how he could not wait to train Leia, as she had all the qualities of a good Jedi, unlike Luke. However, after Obi-Wan died on the Death Star, his spirit went to Degobah, where he convinced Yoda that training Luke was the better option, saying that Leia wasn't ready yet, but Luke was.
Darth Vader/Anakin wasn't aware of Leia's existence as his daughter until shortly before his death, but I believe he cared just as much for his daughter as he did for his son once he knew of her existence ("Tell your sister you were right...")
Abrams says Princess Leia chose not to train in the ways of the Force. In the films, while Luke trains to become a powerful Jedi, Princess Leia is kept busy by essential duties of her own. Later, as the leader of the Resistance, General Organa has her hands full with tasks that don't involve any use of the Force.
Instead of being in the life suit, Vader looks like an older Anakin who never received the devastating injuries, and Padmé and Luke (who struck down Palpatine) are by his side. It's during these visions Palpatine realizes Luke - who he only knew as the Rebel who destroyed the Death Star - is Anakin's son.
Luke, Leia, and Han are on Endor. First, Luke tells her Vader is his father. Her first reaction is one of slight revulsion, perhaps even of him. She gets a very concerned look on her face.