No, I don’t think she really thinks you hate her.
I’ve had very similar experiences with my teenager. He only says things like that when he’s mad. It’s hard to keep emotions under control in those times, but it’s really the anger talking. I’ve see more and more that emotions flood in with ADHD, and he tends to act on these intense feelings right away, where other people could filter through things, and realize that their parents don’t really hate them, even when things seem rough at the time.
I find my son says things like that (at least partly) to get a rise out of me. I just remember that it’s the anger talking, keep firm and steady, and consistent. I will calmly tell him, of course I don’t hate him, I’ll ignore it as much as possible, or I’ll just say we need to take a break and talk about things later.
I highly recommend the book “The Power of Positive Parenting” by Glen Latham. I think, along with the articles you mentioned, will give you the tools to know how to handle it.
I’m glad to say, my son doesn’t say stuff like that much anymore (he’s 15), unless he’s very, very upset. But now I know from experience, that the storm will pass, he knows I love him and I’m there for him, and things will get better, so it’s much easier to handle.
Best of luck! Hang in there!