HI harald - just come across this thread and wanted to say that you do really sound exhausted. It is entirely possible that you are suffering from PND and really need to get some professional advice on that form your Dr.
Do you think you set the bar quite high with regards to your DD? Did you imagine everything was going to be perfect: your DD, yourself? I ask purely because we often have seriously unreal expectations of motherhood and parenthood and beat ourselves up when we fall short - that can often spill over onto our DC.
Reading your posts it does sound like you have settled into a spiral with your DD. You have behaved poorly (through tiredness, hormones etc etc) and your DD has learnt to respond in the same way, which leads you to react to her and so it goes, back and forth, getting worse as you react to each other.
I myself have been known to have a fairly quick temper (in the past) and found myself flaring up with my DS some time ago, his behaviour became even more inflammatory and I reacted even more. It was only when I took a few steps back, quit reacting with a temper to my DS that he also calmed down and responded nicely to me. Their behaviour is learnt from us and they respond to us.
Please consider seeing your Dr to check on PND. You have done the right thing in acknowledging that you have slipped into behaviour that is not acceptable and are doing something about it.
Best wishes harald