welcome to mn.
It is very hard to comment without knowing you and the head.
I am an ex teacher and currently a parent governor and I have seen this from both sides, and of course we have no idea if you are one of the reasonable parents, or one of the unreasonable ones.
Sorry, not trying to be mean, just that this is anonymous.
But I can reasure you that the school cannot get rid of any kids because of parents behaviour. They have a duty to teach the kids on role. The only way they could get rid of your kids is through a permanent exclusion which would be due to their behaviour (extremem behaviour) and totally documented and assessed by the head and the chair of governors etc .
from what you have said that is not going to happen.
The school can ban you from the playground, and in extreme situations put a restraining order on you.
The governors are not 'in her pocket' but do have a duty to her and to the school, and must follow the guidelines.
It woudl be a very unusual situation to have you only allowed to communicate through the deputy, and I am not sure the school would be happy with it.
Lastly (sorry this is a bit long) I have 3 dc who have been through our local primary and youngest is now in year 4. I can only think of a few occasions in the last 9 years that I have needed to speak to the head, as opposed to speaking to the class teacher.
If you have a child with SEN, and therefore need to speak to her often, can I suggest you get someone, eg a friend to be your advocate and come to meetings with you (agree with the school).
If there are behaviour problems that you are being called into school regularly for then you probably need to think about dh being the one who goes into school on your behalf