In your scenario, Obi-Wan Kenobi revealing the survival of Luke and Leia to Darth Vader adds an intriguing layer to their relationship and the tragic outcomes of their previous encounters.
After their fierce duel on Mustafar, where Obi-Wan and Anakin Skywalker (now Darth Vader) had their final confrontation, the emotional weight of Obi-Wan's words could have a profound effect on Vader.
Obi-Wan's admission about the children being hidden would spark a whirlwind of emotions within Vader. On one hand, there would be a flicker of hope—something that he thought he lost forever. On the other hand, the pain of losing Padmé Amidala would be compounded by the knowledge that he could not be a part of his children's lives.
The fact that Obi-Wan chose to withhold more details would leave Vader in a state of turmoil. Questions would flood his mind: Who are they? How are they hidden? Why didn’t Obi-Wan tell him more? This ambiguity would only deepen his internal conflict—part of him would still cling to the idea of redemption and family, while the other part, consumed by anger and grief, would drive him further into the dark side.
Vader's curiosity would manifest in his relentless pursuit of knowledge about his offspring, pushing him to seek out any information he could find, even if it meant further embracing the darkness. This could lead to a narrative where Vader's quest for his children intertwines with his continued descent into tyranny, creating a poignant contrast between his fatherly instincts and his actions as a Sith Lord.
Ultimately, the tension between hope and despair would continue to characterize Vader's journey, laying the groundwork for potential redemption in the future, especially as he grapples with the truth about his children throughout the Original Trilogy. The revelation of their existence could serve as a beacon of hope that, one day, he might reconnect with them and seek forgiveness for the path he chose.