Sunflower Painter.
I wish I could tell you how to do the "oh I'm sorry" method of child care for unruly children but it would not be allowed here, maybe you will figure it out. You are going to have to learn to be clumsy. It doesn't sound as if they will respond to kindness. Maybe a combination of both.
It seems no one is going to want this job. I wish you could leave it for a more stable job in that field.
There are probably ways of coping but I fear the situation will never be good.
I saw my therapist today and we talked about the panic triangle. It ia a three pointed triangle with "situation" (trigger) at one corner, "thought" (anxiety) at another and "panic" at the third. Any one can influence the other. In other words although it usually goes situation, thought, panic it can go the other way. Panic, thought, situation. In other words having a panic attack can influence a thought which can influence the situation that originally caused it. The triangle can also go the other way. The situation can cause panic which can influence thought. (I had a panic attack so now I will have another.) Changing any one will change the others.
Since you can not change the situation, you are stuck with thought, or panic. Thought being the anxiety part of the equation you might be able to reduce it with relaxation or positive self talk.
I'm so sorry you can not change the situation by getting out of this job.
Davit.