Ok, this might be completely off the wall, but could she feel under pressure?
There's a condition called 'Pathological Demand Avoidance'. I'm not at all suggesting your DD has it, but some of the techniques that can be used for a person with PDA are really very useful for children who are feeling under pressure.
My DD3 (3.4) is fiercely independent, and so headstrong that she can find herself picking a fight over anything. She can pick a fight over the apple that she desperately wants, but because I've given it to her, she has to say she doesn't want it, because otherwise she's agreed with me 
So, some useful techniques:
-Don't directly ask her to do something, just talk about how it needs to be done before you go. So, for example 'right, I'll get my shoes on, otherwise I'll be late. Everyone needs their shoes on...'
-Don't directly praise her, but make sure that she can hear your praise of her. So, for example, saying to someone else 'did you see the picture DD drew? I thought it was fantastic.' That way, she can receive your praise without having to respond to it.
That sort of thing, anyway.
I suppose what I'm saying, is that right now, your posts seem to be about how she needs certain behaviour to meet your expectations. What she needs to know, is that regardless of whether you get any benefit from it, she's still important.