You have my sympathies and imo YANBU.
I started a thread just like this, about 6 months ago, with a year 7 child, who I wanted to do an hour a day including reading. Quite a lot of posters really jumped on me. dd has basically said that she felt that it was unfair and nobody else had to do extra work.
I backed off a bit after that, and dd was very happy. Til she started bloody falling behind again! My dd isn't particularly bright, has no motivation whatsoever to work, would rather sit in front of screens or hang out with her mates non stop. She struggled with year 7, we worked our arses off with her to pick her grades up, and then she started feeling hard done by.
Since she had caught up, I let things go a bit, relaxed a bit on the amount I wanted her to do. She pushed more, so I said, fine I give up nagging - you can organise your own work, and do what YOU think you need to do. She drew up a calendar, made plans and promises. She then went into free fall - has had three detentions this half term for not completing homework and fell so far behind that she even tried skiving to get out of school because it is such a struggle.
We're now back to square one, and she is very unhappy because she is so behind. Her report was diabolical. I've spoken to the teacher and he isn't happy at all, and I end up feeling like a failure for letting it go, and he suggested that HE would supervise her for extra work sessions during breaks.
The only thing I would say is I think at Year 9 she should be able to set her own work. I don't tell dd to do xyz, we discuss what she needs to work on, I source stuff like books or websites, and I leave her to work through it to her own schedule. I don't think you should dictate what she reads neither. Just because she is at a certain level, doesn't mean she wants to read at that level all the time. dd reads some real trash, and every so often I will suggest something a bit more intellectual for her to try. I want her to enjoy reading rather than it just be a task.
I do really believe that a set period though where they do have to work, like it or not, does work for some children. While we enforced it, dd was getting her homework done, and producing quality pieces. She had caught up so much.
I also won't do anything for dd if she is rude to me, and she wouldn't dare shout or scream at me. Do you spend any one to one time with her? It does seem like you have a very difficult relationship with her at the moment.