What was the reason for Harmony's sister's death?

Dexter wasn't just having sex with an unknown girl, he was having sex with the unknown girl that was playing his daughter the day before. As part of Dexter's scheme in killing his own daughter he hired the pink-haired woman to play his daughter as a ruse. Then at night he had sex with her, which Harmony's sister saw and thought that he was having sex with his own daughter.

Add into this that Harmony's sister was actually abused by her real father (Harmony's father) during her childhood. Harmony once told her, in an effort to cheer her up, that her father wasn't actually her real father (but he was) but that she was the daughter of some young unknown actor (the young Harlan Dexter).

So after years of believing Harlan Dexter was her real father and the only hope for a happy family, Harmony's sister actually looked for him and found him having sex with who she believed to be his own daughter. Seeing her "new" father be the same sexually abusing character as her other father completely destroyed all her hopes and drove her already unstable personality to end her life.

This is actually explained to Harmony by either Harry or Perry at the end:

Your sister was convinced that Dexter was her natural father so she started following him, hanging around...Do you see where I'm going with this?...One day your sister came calling, and she saw Dexter in bed with the pink-haired girl. What she thought was father and daughter. Remember, that's how it would appear. It was too much for her. First the old father, now the shiny new one. She couldn't handle it, and she took her own life.