I think Lynn is right on about not taking it personally. Easier said than done, though, if you are worn out. (And I am frequently worn out!) I will have to be better about remembering that!
You said you give her timeouts and such. I've resorted to a lot of threatening lately, and it doesn't work, like you said. I'll tell you something that HELPS . . .you say the first part of what you normally say, but leave out the threat. It's not perfect (there are better ways of phrasing things than "Do not ____") but when you are worn out, it's better than completing "Do not __ or x will happen." When I said just the first part recently, DD said, "Or what?" And I said, "Or nothing. Just don't do it." It felt so much better than adding the threat, and DD stopped.
One of the things that has been helping is a wish list. Most of DD's difficult behavior is that she doesn't get what she wants when she wants it (she's got a lot of ideas I can't keep up with). It's understandable. So, what I do now is post a wish list on the refrigerator, and she fills it out when she has a request. Some things I can agree to (like she wants me to stop brushing her hair), but the kitten is going to have to wait, as we have 3 cats now (and one is hers, that WAS a kitten last year).
I think 6 yos can be VERY reasonable . . .eventually. So, if there is some way of letting everyone cool off without any hurting being done (angry words from the parent), and then come to having a discussion, I think it really helps. Maybe we could establish some sort of system ahead of time with our 6 yos to make that happen? Like a signal that a cooling off should happen, and then let your DC pick a "safe space" ahead of time to cool off, and you do the same? I dunno. I'll talk to DD about it tomorrow and get back to you!