In the "Obi-Wan Kenobi" series, Obi-Wan Kenobi does not explicitly reveal details about Padmé Amidala or their children to Darth Vader in the same way you've described. Instead, the series focuses on Obi-Wan's struggle with his past, his guilt over Anakin Skywalker's transformation into Darth Vader, and his attempts to protect the remaining Jedi and the future hope represented by Luke Skywalker.
If you're referring to other Star Wars media, such as the "Revenge of the Sith" film or external sources, Obi-Wan Kenobi does inform Anakin (who becomes Darth Vader) that he has failed, and Padmé dies shortly after giving birth to the twins, Luke and Leia. However, there isn't a moment in the "Obi-Wan Kenobi" series where he directly communicates these specific details about Padmé or the children to Vader. It’s important to note that Obi-Wan keeps the identities of the children a secret for their protection.