My heart goes out to you. I have a child (older) and we go through the same thing. No matter how much theraphy we've had, she still would push me to my wit's end and still does it. When she tells me she hates me, I tell her that she is obviously angry, but I have not and will not change the rules. It breaks my heart that I am "hated" so much, but, I have had to step out of it emotionally. It was tearing me apart. She does not say it that much anymore because I have her complete what I have asked her to do. I do not let her get away with not doing a chore, etc.... unless she is sick. I use a firm voice !
Unless someone has a true understanding of depression in their home, it is so hard to comprehend.
However, I do not allow her to say it or anything like that when we are not at home. Otherwise, the phone is mine.
I have a rule in my house that the phone w/ texting goes on the kitchen table at 10pm. She says I am the meanest. I have never let up on that rule. She needs her rest and I can't have her fall apart in school if she is tired. In fact, last Thursday night I woke up at 1:50 AM and I pressed the button on her phone. All of her friends were writing to each other. Can you imagine? That's what they do if the parent doesn't step in and make rules.
Therefore, have a few rules and expectations. Make sure she is doing some chores. Be consistent when she needs to do her chore, etc...
When she does comply tell her thank you at least twice.