I've only read the first page of posts in this thread, but I tend to agree with the posters who say to let your DD run with her homework independently if that's what she wants. Here are my thoughts on your concerns about her mistakes, and her refusal to work with you to correct them.
I can easily picture us being in this situation with our DS6 at some point (he is super resistant to us working with him, but isn't focused enough or reading well enough to do homework independently yet). If he weren't getting reinforcement from his teacher that his errors or sloppy output need correction, I'd take a few minutes at some other time in the week when he's not doing homework, and have a serious conversation about how we feel about his errors/sloppy work: how we understand that his teacher seems to feel this is okay, and how our values are a little different; how we feel that we should keep learning and correct our errors when we can do so, and how working with dad and me would let him learn more accurately as he moves through school; that ultimately it is his choice whether to do this or not, but that we don't agree with his current chosen approach.
Ultimately, it's her choice, but you could share your feelings with her, so she can consider them.
