Barbara Gordon should not be confused with the character who becomes Batgirl. Traditionally, this would be her daughter, also named Barbara, but Christopher Nolan never took Gordon's daughter to that conclusion.
Full name in comic continuity is Barbara Eileen Gordon.
She, her husband, her kids, and The Joker were the only ones who know that Batman is innocent of Harvey Dent's crimes, until the truth about Harvey is revealed by Bane.
In The Dark Knight Rises, she and Gordon have separated, having taken the children with her to Cleveland. This is most likely reminiscient to the comics, though unlike in the comics where the divorce was a result of an affair on Gordon's part with another female officer the movie states that it was due to Harvey's attempt on their family that caused the divorce to occur, as well as likely being unable to deal with hiding the truth about Harvey and watching the man who attempted to murder her and her children continue to be glorified.