How did Leia take to the idea that Vader was her real father?
When Luke found out that Vader was his father it shocked him. How did it affect Leia. She found out that Luke was her brother, I'm sure it took some time for her to adjust to? How did she feel about Vader being her father?
Luke reacted as strongly as he did because he was told by Vader himself at the end of an exhausting duel, when for all he knew Luke still might have lost his friends (all he had left in the galaxy after his aunt and uncle were murdered), and after the emotion of leaving his training. Had he been told by Leia during a quiet break in the action I bet he would have been much calmer as well.
Its something that Leia would need to process for a while and she would have some confused emotions I am sure.
For Luke also played the concept that he had an idea about his father. First as a pilot of a freight cruiser, then as a great Jedi Knight, pilot and hero of the Clone Wars… and then Vader, evil incarnate.