I haven't read that book but it sounds like a very good approach. I was going to say that it sounds like you need to get her on your 'team' a bit rather than it being strictly parent/child; have discussions with her, ask her for her opinion or what her suggestions are.
I sort of HAD to take this approach with my ds, he pretty much demanded it and expected to be included! It's worked a treat though because we are used to negotiating and it's second nature now.
Just things like when you get her from pre-school, she can choose from two options you give her for lunch (or if you're brave she could choose what she likes). If she cries at the dinner table get her involved; "shall we sit here or have dinner outside today?"
I imagine she is saying she is tired because she cannot actually articulate the subtleties of what she's feeling, which may be "I wish I was a grown up like you mum, and could choose what to do much more and have some control".....
I think give her more control and ask her more for her suggestions; if she has to get out of the bath, for instance, focus on her next choice - what will she wear for bed, what snack will she choose, etc etc.
This approach has certainly worked for me, anyway. Ignore me if you've already tried it all!