Her name is Helena Kyle. She has a surprisingly normal life. A couple more kidnappings than most kids go through, but when you get a nearly murderous Batman, the entire JLA, the Birds of Prey, the JSA and the Outsiders on your case forty seconds after you've taken a baby, kidnappers soon realize that it's truly not worth the risk.
She is smart, and pretty soon she realizes that her mother's income doesn't match her expenses. She is also straightforward, so she asks, and she soon learns who her mother was and what she used to do. She thinks it was cool, but says that *she* will be a firefighter and an astronaut.
Batman shadows her first boyfriend. Then her mother talks to Batman, and it doesn't happen again. She has to find another boyfriend, of course, but that's not too hard.
She fights a lot with her mother as a teenager, and says things that she actually meant. She never runs away, puts on a costume or tries to rob museum to prove a point, but there is no amount of bodywork that will make that car look well again. Both Helena and Selina are very scared by the accident, and things sort of calm down between them.
She goes to Harvard and ends up a lawyer. She never cares much for cats and she thinks bats are ugly, and takes her mother's bi-weekly visits with patient equanimity.
She's reasonably happy.
Selina smiled as the baby reached for her image in the mirror. It was a complicated plan, but she had pulled off crazier ones.