I get how your wife feels. I don't hit my son. There has been days my stress level and being tired. All the feelings that parents go threw with having a special needs child. I don't have help with my son. When you deal with the behaviors every day it does wear you out. I would lie if I said I never hit my son. But after it happened I felt very bad. The toll of everything you go thru every day gets the better of you. I had started my son on some new medicine (Qelbree). After a couple days being on it I and my sons school have noticed a little bit of change for the good. I have heard great things about the medicine and my oldest takes it for his anxiety and ADHD. It has helped my oldest alot.

Things are going to fast at school for him.
He needs a 'Cool-Down' time of 5 to 15 minutes between events so he can collect himself before going to the next task.

I disagree with the previous commenter. I think it’s a normal reaction from a parent whether you have a neurotypical or autistic child of that age. I don’t know how receptive he is or his cognitive level, but I feel it’s beneficial to use behavior modification to control unruly or harmful behavior. Especially if they are exhibiting this behavior at school and to other children.

I also go through this with my granddaughter, and what I noticed with her is that if I show any aggression back to her it just makes her twice as bad. I did smack her butt one time after she was hitting me and she just came at me even worse. The calmer I stay with her the quicker she'll calm down.

You need to speak to counselor - it's good she didn't lie to you but you need best way forward and better ways to deal with like behaviour therapist or school advice or specialist school in challenging behaviour