Kelly Carlyle is the daughter of Steven Carlyle with his first wife. After the divorce, the mother got the custody of Kelly and her sister Chris.
When Poison Ivy managed to mind-control Steven, she used his DNA to create replicates of him. The replicates would first be kids and Ivy used some of the children replicates to disguise them as their "sons". During her charade as a reformed criminal wanting to settle down with her new "husband" and "sons", Ivy introduced Chris and his "brother" Kelly to Batman as they noticed the Batmobile outside their house. The fake Chris and Kelly seemed to act like how most children acted when they saw Batman, thinking it neat that he came to their front door. In Kelly's case, he and Chris were hoping that Batman would take them for a spin the Batmobile until Ivy told him to leave the Dark Knight alone, ushering him away as they needed to talk.