tbh, I am not sure that posts telling the op that this is the beginning of the end and she is living with a murderer are helpful. As much as they might be designed to shock the op into doing something they do also come across as incredibly aggressive. There is no disputing here that the op's h's actions last night should be a deal-breaker for anyone, however according to the op this is the first time in what has presumably been a long-term relationship of several years, given that they have two dc together.
Only the op knows the history of this relationship, but if there have never been any incidents like this in the past this will be an incredible shock. This is the man the op has trusted, who is the father of her children, someone she says has never shown violent tendencies before (and we have to take her word for that, making assumptions that he must have shown controlling behavior in the past are just that, assumptions, we don't know, and if the op says he hasn't then it's not up to anyone to tell her she is wrong.)
Op, it's understandable that if this is the first time then you are in shock. And if there have never been any signs that he is aggressive then this is even more of a shock and you of course want to believe that this is a one off. And perhaps it is. Perhaps he is incredibly remorseful and will seek help for his aggression and will swear never to drink again so as not to repeat history.
But ask yourself this, what would it take for you to genuinely trust that he would never do this again? Having done it once, what makes you sure that he would never do it again? Can you be sure really sure that he would never again lay a finger on you?
Remember op, you are not the one who has to let him back, he is the one who has to prove, beyond all doubt that he will never do this again.
The thing is that when a line is crossed there is no way back from it. Even if your dh went to every length to prove that he wanted to change, you can never change what already happened. Do you want to live with that memory for the rest of your life? And if so, why? What is it about him that makes him worth forgiving an action which could have killed you?
I am of the view that all violence is wrong, however, I do also believe that there are levels which someone can come back from. what I mean from that is say a couple has a heated discussion and one party slaps another and instantly regrets it but it's done in the heat of a moment, then there might be a way back. Or if one throws a glass of water over the other for instance. But then you enter into the realms of degrees of violence. If a slap became a punch there is no going back IMO. One can be seen as an impulse reaction. not ok but a lashing out, and assuming it was discussed could potentially be gotten over in time. But once that violence becomes more deliberate it becomes impossible to explain. Strangulation is the level at which it should never be written off as a one off, because it's a one off action which could potentially be the first and last time - iyswim?
Wanting to keep your little family is understandable op. But the truth is that this isn't your little family any more. he strangled you. He betrayed the trust you have in him. Being in bed next to the person you love should be the place where you are secure, where you feel safe, and he has taken that away. Your family unit has already changed op. You can't undo what happened last night or even come back from it. So now you have to move forward back to a place where you have that safety and security. And as he has taken that away from you that place shouldn't be with him.
If he is genuinely remorseful over what happened then he will leave the family home without question.