Like most parents, Esther Jenner cares first and foremost about the happiness of her children.
And on the day that Caitlyn Jenner revealed herself on the cover of Vanity Fair, her mom was bursting with pride.
"It was a wonderful day," Esther tells PEOPLE exclusively. "It takes so much courage to do what she's doing."
Esther, who visited Caitlyn a week and a half ago in her Malibu home, recalls an emotional moment. "When I first saw [Caitlyn]," says Esther, "all I wanted to do was give her a big hug. It was such new information."
And adapting to that information has been a process, Esther admits. "It takes some time getting used to. I've called [Caitlyn] Bruce since the day he was born. It's going to take some time, but I will adjust."
Most important, "I love her," says Esther. "And she's happy. That's all that matters."
For much more on Caitlyn's journey – including a candid interview with her daughter, Cassandra, and exclusive details on her next moves – pick up this week's issue of PEOPLE, on newsstands Friday