Sounds like you're just starting to get professional help. The child psychiatrist will be able to help you with learning different ways to manage your child.
I've had experience with children who react with violence. What I learned from a social worker is to calmly and firmly physically restrain a child before they get out of control. There is a specific technique during which you wrap your arms and legs around the child. It's called a therapeutic hold. I can't describe it accurately. Perhaps one of the professionals can show you how to do it.
The plan is to hold them until they calm down. The holding is the consequence. It deals with the immediate situation and also helps them learn how to calm down. It has to be done with as little emotion as you can muster.
At 4, he is small enough that you can safely enclose his arms and legs with your arms and legs. I would hold the child with his back to me, wrapping my arms around his torso. Grab each wrist and cross his arms over his chest. Then wrap your legs over his legs. Sit down with him in your lap. It will take some time to learn how to do it so that he isn't able to squirm free.
One of the reasons this works is that he senses he's out of control. He doesn't like what is happening any more than you do. He just doesn't know how to get his emotions and thus his body back in control. He will eventually be relieved that you are in charge, that you will help him get back in control.
He is doing this at home for many reasons. An important one is that he knows you will love him no matter how he acts. He has to have an outlet somewhere for his intense emotions. Also, school is a more structured environment. Many children function better with more structure and less stimuli. You can't maintain the same sort of environment at home.
Now that you have professionals involved you'll learn ways of managing his behavior and he'll slowly learn better ways of behaving. My grandson has some of the same issues as your son. He started in treatment when he was 2. He still has difficulty with anger but we've all learned how to manage it.
My grandson started in treatment thru the school district in an early intervention program. A social worker came to the house every week and showed my daughter how to interact with him. She taught my daughter discipline skills that worked better than the ones she was using.
One way that my daughter manages her children is to send/take them to their room when they are not managing well. At first she would physically have to take her son to his room but after just a few weeks he would go on his own. I think he was around 6 when she started this.
I suggest that you could try it with your 4 yo. Notice when he's barely starting to get agitated and take him to his room to calm down. Better yet monitor activity and mood and provide him with a safe place in which to be calm. These kids are so easily agitated. They do not function well with alot of activity going on at once.
Let him know ahead of time that you have a new plan to help him manage; that when he needs to settle down you are going to take him to his room. He can play while he's there. It's not a punishment. It's a management tool.
I'd ignore the lies. He's doing it to get your attention. I'd not take action based on his words. Don't go to the neighbors for example. When he says mommy hit me, respond with "I know that's not true" and then ignore any further statements.
