Barbara Gordon grew up with both of her parents, her father being the commissioner for Gotham Police. She grew up with a strong sense of Justice and always wished to help her father as she grew up, but he always refused to let her get involved with his work. During her adolesense she gained wind of the Superhero Vigilante, Batman and was inspired by his individual heroism. Barbara then decided to follow him from the shadows and eventually created the vigilante sidekick, Batigirl.Batgirl tried numerous times to get herself to become batman's sidekick, he always refused and forced Batgirl to return to her home, but never revealed her identity. Convinced that Batman was simply being stubburn she persisted and learned to hone her skills in combat and technology. She tried again to prove herself and eventually did so by helping him to defeat Poison Ivy, Batman allowed her to become his protege but refused to provide her with any formal training and also kept his identity a secret.
Despite these actions Batman did trust Batgirl, he was simply concerned for the commissioners daughter's wellbeing and if anything should happen to her it could trace back to Batman and ruin his entire cause. Throughout the years Batgirl proved herself to be a capable sidekick which inspired Batman's choice when he adopted Dick Grayson and made him into his young sidekick, Robin. Batgirl and Robin both grew up together as fellow sidekicks, and after Robin's enlistment Batman allowed them both access to the Batcave and finnaly his secret Identity.
As time passed, the Bat Team began to become more and more about Batman and Robin rather then Batgirl. Even though she maintained a close loving relationship for her mentor Batman and best friend Dick Grayson, Batgirl felt her time as Batman's sidekick unfullfilling and began to act as her own Superhero. Dick was disapproving of this but Barbara felt this was nesscessary, causing Dick to blame Batman. Batgirl's actions caused her to come to the attention of the Joker who would kidnap her father. Having lost contact with Batgirl and Robin, Batman confronts the Joker himself but is followed by the commissioners daughter.
In order to draw Batman away from the situation The Joker planted several bombs throughout the city, instead of helping Batgirl save her father, Batman chose to fall for Joker's gag bombs which intern allowed Joker to shoot and paralyze Barbara Gordon. This intern caused Robin to become very angry with Batman and leave his side and the mantle as Robin.
Several Months later Barbara was released from the hospital and simply forgave both Batman and Dick Grayson (now Nightwing) for the Joker's actions, feeling it was in no part their faults. Barbara still maintained her love for justice and decided to return to Batman's side with his new Robin, Tim Drake as Oracle, their hacker and operator. She developed a new relationship with Tim as the new Robin and felt for him as a little brother role much like with her time with Dick, giving Barbara the drive and passion she needed to become the perfect operator and remained in the Batcave.