What you describe sounds very familiar to me. I had all that with my DS1 and also went through everything you describe - cajoling, distracting, etc.
I can believe, sadly, that you had such an appalling thing said to you as "this is all your fault". What a dreadful thing to say and what astonishing lack of empathy and understanding it shows.
When you say your DD liked the structure of the school environment, but hated the chaotic, noisy bits, it does make me think of ASD, simply because this is something we had to consider for DS. Have you looked into this possibility at all? (Hope you don't mind me mentioning it).
What is it that your DD misses about school? My son said he missed school recently, but it turned out he wanted more company with children of his own age, not school itself. We are working on this.
Why do you think you are not doing home ed justice? At eight, your DD does not have to revise for GCSEs, so there doesn't need to be any pressure. Maybe you feel as if you should be teaching her for more time or in more depth? From my experience, and that of others on this board, home-educated children can get more done in less time than schooled children.
If your DD would prefer more structured teaching and you need more time to work yourself, maybe an internet school would help? I have seen Briteschool discussed here for primary-age children.
Must go to bed , but am happy to help if you have any more questions.