Hi sonnet I hope your week is progressing ok.
It sounds as though you did well staying calm, I think you are right about it being the key to a generally calmer atmosphere.
It is disappointing that the school seem to think they dont have to take responsibility for homework. They set it at the end of the day so they should be consistent in their approach to getting it back.
I agree with bigbuttons about looking for positive things. When she does her homework [with or without a fuss] praise her for completing it and try to comment as little as possible on the quality of it.
Many children find homework really hard, it is the home is home, school is school thing.
If you are concerned about her standards of work I would make an appointment to see her head of year or form teacher.
At the end of the day if she is working well at school then she will be showing them what she is capable of at school and so long as you provide her the opportunity to do her homework then you are showing the school that you are supporting them now they need to show that they are supporting you.
There has been some research in to the actual benefits of homework and I am pretty sure they found that there was very little value to it.
We hate, hate, hate homework in my house
Keep up with the calm approach and good luck