Oh man!! I wish I could work with your daughter!! I hate hearing that school work is causing so many issues. There's something going on that's causing her to hate it so much and she needs a re-set!
@Juliestcyr is spot on with her advice.
Totally not a fan of the reading grade based on those AR tests.
Ideas popping into my mind ... If the teacher is not able to work with your daughter about finding an alternative way to assess the reading, then you read the books with her. Take turns reading pages maybe? Talk about the book. You say the comprehension is there. Perhaps emotionally connect with the book so she retains it better for that stupid test.
Then... as for her independent reading homework ...
She's 9? Is she in 4th or 5th grade? The expectation is probably 20-35 minutes of reading a night. Empower her to tell you how she's going complete that. In my reading/studying for literacy development, this should be done earlier in the day (not right before bed). 10-15 minutes before school. Another 10-15 minutes right after school. While dinner is cooking. In the car. Wherever/whenever. Also she chooses what she reads. Blogs. Newspapers. American Girl magazine/books. Cooking websites. Fashion. Animals. Sports. Cartoons. Disney Channel gossip. History. Biographies. How to draw. Books on pets. Mysteries. Realistic fiction. Goofy young romance... the tween version of book soap operas.
What's her assessed reading level? She's at a transitional level right now. If she's weak in any areas, the books she can read might be too babyish and the books that she thinks she might want to read are just a little too hard and it it takes too much effort to hold onto the story and she gets bored/frustrated/loses interest.
When my daughter was in 4th grade, she dropped low on her reading. She was in the lowest level of books in the teachers' library. It was about the time of Twilight. (Please don't judge...haha). I read the book to her and then before we moved onto New Moon, she had to read Twilight herself. Was it the best literature? Of course not. BUT the reading level wasn't too hard, she had heard the story and had already been able to put the picture in her mind. (I think we had seen the movie too so she had those visuals as well). Then really that ginormous book (for her) was an exercise in practice and building reading stamina. By the end of the year, I got her reading level back to grade level. For her, understanding the inferences and connecting what was literally said and what you were just supposed figure out from the story based on what was unsaid was (and continues to be) a challenge. When she misses that, the story just doesn't make sense and she loses interest.
Can you sit down with her maybe and have a "grown up" talk. Talk about how you hate how homework is going and you are sure she does to. Then get her to come up with solutions to solve the problem. Be open to her suggestions and tell her that you'll try them and then talk to her about how they are working in a couple weeks. (Even if you have a feeling that they won't). Try them, see how it goes. Lay off the fighting. Maybe empowering her might help. Now's the time in 4th and 5th grade to get this power struggle fixed before middle and high school!!
My thoughts are with you during this challenging time!! Good luck!!!!!