When Heather realizes what's in her necklace. Even in death, Harry is still looking out for his little girl.
When Douglas compares Heather to his dead son, Heather subtly implies that she'd like him to consider her his daughter.
Really, the development of their relationship in general. Understandably, it got off to a pretty poor start - Douglas relentlessly pursuing Heather on Claudia's orders despite Heather's rather justified mistrust of him - and it reaches a head by the time Heather finds her father murdered in their apartment, where she and Douglas both seem to realize that it's partly because Douglas inadvertently led the cultists right to her front door. Still, once things calm down and begin to come to light, they begin to trust each other, with Heather opening up to him about her past on the drive to Silent Hill, and even sharing a rapport with Douglas by the time they split up to investigate the town. Probably helps that Douglas shows genuine remorse for his (however unintentional) part in Harry's death, and is sincerely determined to help out Heather however he can.
When Heather phones her father at the start of the game, she finishes the call by saying "I love you too, Daddy."