The Huntress has one of the more in-depth stories in the Batfamily, mainly because she's been interpreted in many ways. Some have her as the daughter of a mob boss who seeks to get revenge and dons the Huntress attire to strike fear into them much like Batman does. Others see her inspired by Batman and dons the outfit to get her own brand of justice. And in a recent cause, she's the actual daughter of Batman from Earth-2, and only becomes Huntress when she's accidentally sent to Earth-1, and wants to hide her identity.
In either case, she has a tenuous relationship with Batman, while other members of the family are actually quite honest and kind to her. She's served on the Birds of Prey, worked with numerous Robin's, and eventually even got the respect of Batman when he sponsored her to join the Justice League.