I don't have children, but I am an aunt to 2 wonderful girls who grew up in a home with an alcoholic father, and I hope you do not feel I am out of line for sharing this to you - and it will be a long post.
I used to hear absolute horror stories from their childhood, via my sister (their mother), primarily about how he treated her (I didn't really hear what he directly put their kids through until much later). I heard stories from her for years, gave advice, saw it ignored, and finally cut her off by saying that I couldn't bear to hear her go through that anymore without her doing anything but vent to her family and wake up the next day and let the whole cycle repeat.
I don't know if that was the right thing to do, but she finally left him later that year. However, a lot of damage had already been done to both herself and her children. Both have had issues with control, because they lived in a household that was out of control. One went mute for several years - not speaking a word to outside family members. The other battled anorexia and addiction (and I'm proud to say that this past Sunday, she received her 1 year sobriety chip).
My sister and her ex started having issues and she started talking about separation when her children were young - it finally happened when they were in their pre-teens. A chaotic household does a number on children in their formative years. I've seen it from experience.
I had the privilege of saying that to her, and watching her decision without being in it, too. Looking back, I don't know how she felt about that. I felt I was abandoning her, but I couldn't listen to it anymore. Ironically, I put myself through the same mess, sans children and marriage, several years later before I finally got a glimpse of what she was going through.
Having been in a relationship with an alcoholic was eye opening, but having been in a relationship without marriage or children was very easy to break. I can say that knowing precisely how hard it was for me to break that relationship without those additional roles of spouse and parent. But I also saw, from my sister's experience, what it was like to be in that role.
I was also able to see the damage done, from the outside looking in. Not only to her, but to her children, in their formative years. And I'm trying to relay that experience I've seen on the outside looking in the best that I can. For her, there were 4 people suffering, but 3 that couldn't do a thing except walk away. For me, looking from the outside, it was an easy, obvious decision, but again - like I said above - I wasn't the one, at the time, making the decision.
What I do know is we can control ourselves and our well being, especially in the event that physical harm comes to us. Most states have somewhat lengthy statute of limitations for DV, and a DV charge can be accompanied by a protective order. Meaning that person has to say away from you, and you and your children don't have to flee from them. Documentation of everything that occurs, as mentioned above, never hurts.
It does sound like you may need some time and space to figure out the best plan for your and your children moving forward, so it may be a good idea to look into a protective order. Just for the sake of having some peace for a bit to settle your mind. Living through a situation with an alcoholic partner myself - I can attest to that.
Whatever it is you decide, I wish you the best for yourself and your children. Again, I hope I wasn't out of line sharing my own experience, and I hope you understand that this isn't what I am stating will happen all the time, but simply what I have seen with my own experience.