Sorry to hear that her parents are getting involved. As if the situation weren't bad enough! Since the father has threatened you physically, I would file a police report, especially if you think he would act on his threat. Yes, that could aggravate the situation even more, but a visit from the police could shake up the parents enough that they leave you alone.

I know you don't want to hear this, but I agree with her parents that she doesn't have to do anything. She really does not have to do anything you say. She's an adult and she can live however she likes. According to her lease she probably does have to keep the dwelling clean enough that it doesn't attract insects and rodents. If she is actually that messy, then you do have a legitimate complaint that the landlord should address. Otherwise, you're stuck with putting up with her behavior or moving out. Granted, civilized people will sit down and draw up house rules and work out a schedule for completing chores. However, she's already demonstrated that she won't work with you on agreeing to and sticking to some basic house rules. Disagreements on house rules are a major sticking point for many housemates. That's why people interview potential housemates to see if they're compatible or they live alone.

You say she's moving out soon? Can you hold out until then?