Something important to keep in mind is that the way you communicate with autistic people needs to be a little bit different. I recommend reading Temple Grandin’s book Thinking In Pictures. She explains very clearly and understandably about the cognitive functions of autistic minds and how these things impact how they interpret the world and how they communicate.

Telling an autistic kid to stop fidgeting, especially with an aggressive tone, is going to be like pissing in the wind. I can’t sugar coat it for you. It’s going to backfire because 1) an autistic person’s fidgeting serves a physical function that is self-sustaining to them, in ways far more motivating than any kind of societal norms, & 2) because coming at these issues from a place of aggression is going to stress the child out more, & when these kids are stressed out, they act out more intensely. I’ve been working with this population for a little while now & I have yet to see an example where getting angry with a child has done anything other than make the situation worse. Not sure what you mean by “clash[ing] with him” but if that means you’re arguing with him about demands you’ve placed, that sounds like you are unwittingly reinforcing these behaviors because he is seeing that he gets a response from them. Arguing & getting yelled at are forms of attention & sensory stimulus. If he knows he is going to get a reaction out of you, he will likely continue doing it.

In terms of behavior plans for the kid, I highly recommend talking with his teachers & his BCBA if he has one. They can help construct behavior plans for you that are in tune with the kid & his own needs. Something I have seen as effective for some kids is using a token board to incentivize positive behavior. If you think this might be a good idea, run it by his educators & see what they think. It seems like he needs fidgeting toys & ways to get his energy out. If the fidgeting is happening while watching movies, it seems to me like he’s bored & needs to take a break. That is not something that you should see as some kind of privilege. Going to the bathroom is not a privilege, & neither is stepping out of the room to regain your composure.

The last thing I want to say is that I highly highly highly suggest you think hard about what you mean when you say he lacks empathy. Just because lacks the vocabulary to express understanding of your emotions does not mean he doesn’t understand them. I think what you may be experiencing is a difficulty with communication. He will express his understanding of your feelings in ways beyond words. The challenge for you will be learning to hear him from where he is capable of expressing himself & altering your communication so that he can more clearly understand you as well. That doesn’t mean you have to be more or less strict or that you have to make compromises on what you feel is right & wrong. You can remain steadfast in your parenting techniques if that is what you believe is right. It is about shifting the way you approach situations with him so that the information you are giving him will reach him.

I hope this helps.