i just want to start by saying that my dad is very critical of me, and when i lived with him, nothing was ever clean enough, i was never pretty enough, my straight A's and 1 B was not good enough, etc...
he meant well i'm sure. he was trying to push me harder. i was a constant dissapointment to him because he believed i was able to do much more than i was doing. (its just a compliment in disguise)

do your parents join you in therapy, like a family therapy session? since they are so involved, why not work it out with them in therapy?
it does sound like they're trying to be really helpful in their own way. the goal is a clean house and theyre trying to threaten taking away privledges in order to make you want to get it clean.
it does seem that they are missing the point though. maybe they arent helping in the way you want them to...
since i dont know your whole situation, my only advice (if you want it) is to talk to them. maybe let them know that you need help with the house cleaning.
anyway, if your parents are paying your rent (i assume this cuz the landlord called your dad) then that is a great sign they want to help you.
maybe your therapist can help you figure out a way to confront them without making them feel unappreciated....