Follow your instincts about what he needs. Period. REGARDLESS of what any teacher, principal or 'expert' says. YOU are the expert in your son. Period, end of discussion, no argument trumps this EVER. You have those instincts about what your child needs BECAUSE you are the expert in that child - they are instinct as old as humanity or older to ensure survival of the species. The docs, teachers, principals try to tell you otherwise because they have degrees and/or have studied some field of study. They may be experts in some field of study but they are NOT experts on your child.
Get that psychiatric student involved with taking him out around other kids in the community. If homeschooling is an option, it likely cannot hurt any worse than being in school being told you are a bully and an awful person but never being given any tools to learn other behaviors or positive reinforcements.
As far as why can his mommy come and the others can't - got 3 little words for you: NOT. YOUR. PROBLEM. That is for the school to deal with. Esp as when in school you will be helping the entire class, not just his.
One MAJOR thing that should throw HUGE red flags esp when the child is as young as four:
Your child should NEVER be in a place wehre you cannot drop in or arrange to observe the classroom. Yes, with a classroom sometimes a few days' notice is helpful. But what is going on in that class that they will not let you see? Why is this teacher so adamantly against ANYONE being in the room with her and the children? What is she doing that you or an aide cannot be there to see?
EVERY list that is sent to parents about what to watch for when choosing a daycare or preschool or school for children includes this, at least every one here in the US and I have seen these from at least six states - 3 that I lived in and 3 that I have friends/relatives in. This is actually one of the biggest most alarming red flags from what I have been told. The evaluations are needed, no doubt, but this red flag should at least be discussed with the school. The teacher WILL be unhappy that you ask this but it is a fair and reasonable question esp given your son's fear and reluctance and upset before school each day and her refusal to accept ANY of the ideas that you have come up with or to give him any TOOLS to use to help control and soothe himself when upset. Adults, esp women, are hard-wired to respond when a child is crying and this woman's response is not what I would expect of a teacher of 4 yr olds.
As for the 'give him the idea he can just quit' rationale - hogwash. It will give him the time he needs to mature and learn the tools needed to cope in the classroom. Maybe if you keep that theme up for years he would end up iwth that, but removing him before the end of the year one time hwen he is four is NOT going to do that. If that was the case then there are a whole lot of us who would have all sorts of bizarre behaviors. heck, if doing something one time when four determined your life then my daughter would always prance around like a My Little Pony character on a soccer field. I assure you that she did this for most of an entire SEASON of soccer at age four (while being the only child to get the ball into the right goal more than one time per game and doing that in about 1/2 the games she played in that season. Of course 4yo's playing soccer is sort of like watching chickens run around excited rather than actually being soccer, lol!). She then played soccer for years with-o EVER pretending to be a pony or cartoon character.
I am sorry it is so hard to get the school to provide the things your child needs in order to learn and grow and that this teacher is so determined to not be helpful in any concrete way.
I wonder what the teacher's actions and words would be called if she was evaluated to see if she was a bully?? Sure seems that she is bullying your son, isn't she? And trying to bully you by refusing to allow any real help for him or to try to actually teach him something.