Is his fear of being deported realistic? If so, are you in the same situation regarding citizenship and permission to be in the country?
I am assuming that he could be deported and you would not in my suggestions. Whatever the situation I would still draw a very hard line about any physical abuse, and I would include restraining you, or blocking your access to leave as physical abuse. (I believe the law does as well, but you should check local resources)
In your shoes, I would probably tell him that he has had his one and only chance to do this to you without consequences--you will call the police immediately next time. He needs to control himself in this regard, you will have zero tolerance.
However... . I only recommend doing this if you mean it. If those consequences are too tough for you to dish out... . think about what you are willing to do. And do remember that abuse will tend to escalate if you let it.
When I was up against abusive behavior, and my wife had acknowledged being abusive (mostly verbal, but it did escalate to physical a couple times), I had a very simple HARD statement I made:
The very first thing we are addressing is your abuse. At its core the abuse is about you controlling me. I am not saying that I have no issues to address. I am saying that while we are addressing your abuse, I am not discussing my issues or reporting to you over it. That would be giving you the control that your abuse is trying to achieve.
My issues were off the table for her. Anything vaguely like "I abused you because you X" or "I'll stop abusing you when you Y" is simply not acceptable.
We have gone completely beyond that now, but it really helped me at the time a great deal.
I don't know what to say about moving out--it sounds like either of you moving is currently coming up when you are both too worked up to make good decisions or have useful discussions.
I'd say that the question of whether the two of you will live together is much bigger than the question of which of you moves out. Do you know what you want?
Hang in there--you will make it through this.