What concerns me is the degree of shock and outrage, in posts from supposed educational professionals (I say supposed because I don't think the shock and outrage is professional or warranted)and others, regarding the OP's daughter's refusal, in school, to do a piece of school work, when she seemed to be developing an illness.
Yes, I mentioned additional needs, simply because there are many additional needs which can manifest in a child refusing to do their school work, which teachers will have come across in their careers. My main point is the behaviour should not be that shocking, not that this child necessarily has any additional needs but many children, they will have seen do. For those of us whose children have had some additional needs this is upsetting. I want the teacher's who deal with my child to be calm, caring, capable and well, just, professional.
A lot of posters seemed quick to blame the parent. Yet the OP did not seem shocked that there was a 'battle of wills', as she put it, when her child was issued with a ultimatum. It sounds like she is familiar with dealing with this kind of behaviour, successfully. She knows that ultimatums and punishments do not work for her daughter and wrongly assumed, it seems, that teachers would be able to handle the situation differently.
It would not shock me either, not all children are compliant, not all respond well to ultimatums or punishments, for a variety of reasons, that I spoke about upthread (not simply bad parenting). I would have assumed the some of teachers posting on this thread would have been familiar with dealing with similar behavioural issues so would have more in their armoury than ultimatums and punishment to help support this child.
To me, the criticism of the parent seems just like the teaching profession clubbing together in an attempt to not take any responsibility for dealing with anything less than a totally compliant 5 year old (and parent) or possess any flexibility in their approach to children with differing needs.