In the Comics: Batgirl is Commissioner Gordon's daughter, secretly fighting crime alongside Batman under her father's nose.
But in the Movie: She's Alfred Pennyworth's (Michael Gough) niece.
Does the Change Work: Sure, but only because it's hard to care about which family tree Batgirl (Alicia Silverstone) belongs to in a movie that also features the Caped Crusader (George Clooney) flashing Bat credit cards, flying on falling doors, and going pun for pun with Arnold Schwarzenegger's brain-numbing Mr. Freeze.
On top of that mess, this series' Commissioner Gordon (Pat Hingle) is a dottering old fool, featuring one-sixteenth of the characterization he'd later receive in the Nolan trilogy. Lumping Barbara with Alfred effectively brings her into the fold in the only conceivable manner.