4 YO witnessed Domestic Violence at home and is now portraying this behavior at day care, what can I do to help correct this and support my son?

First actual post.. my boyfriend and I got into a terrible fight in the middle of the night this past Saturday morning around 4 AM. He had come home drunk and irritated, and loud. I asked him to quiet his phone so my son could sleep and basically told me my voice is louder than his phone on high volume and to get the fuck away from him. I asked him why he would want to wake a child up just because he is irritated at his mother, my son was innocent. He pushed my head away from him and said he wanted to punch me in my face. I swatted his hand away from me and got out of bed to leave the room and he snapped, jumped out of bed and into the hallway after me and strangled me for a few seconds.​My son was now woken up by this. We tussled and I did my best to defend myself, because this is not the first time unfortunately that he's come home and this has happened, but it is the first time my child ever saw it take place. Sparing the details, my child was behind this man hitting him in his leg trying to protect me and get him to stop, crying as I was pinned up against the wall. Eventually he released me and disappeared back into our bedroom with the door shut. We have an air bed, so after I held my son and comforted him to stop crying I blew the bed up and we slept on it until the morning when it was time to go to work and daycare and he hasn't been back since. I can barely even type this without crying just thinking about how much of a failure I feel like as a woman and a mom to have put my son in this kind of position.​We've left and have been staying at friends houses and hotel rooms since this happened, but my son has been in daycare since Monday. His sleep schedule has been all over the place from moving around, and he apparently stole a toy and put it in his book bag yesterday. When his teacher found it, he told her he didn't know how it got in there. We discussed this as it is NOT okay to take from people, we have to talk to them about the toys we like we can't just take what isn't ours. He sunk to the ground and started whining, seeming ashamed and defeated. We discussed it a little more in the car but I didn't want to shame him any further in lieu of what's been going on at home and how I'm sure he's been feeling.​Now, today his teacher told me that her daughter was playing with a toy he liked and my son got on top of her and put his hands around her neck and punched her in the stomach. His teacher intervened and asked him why he would do that and he told her he saw this at home, and that it happened to him and his mommy. He wasn't touched by my ex, but I was. I am completely deflated and broken and feel I have deeply disturbed my child, and I have absolutely no idea how to correct his behavior besides long talks and hugs and love. I am in desperate need of advice. via /r/Parenting https://ift.tt/34vb9io