Hope someone else comes along soon. There are some really well-informed people here.
First of all - it sounds awful. Distressing, confusing and just completely exhausting.
I don't know, from your post, what your take on your current situation is.
I think you see it as a temporary situation, to clear your head(s) until you start with counselling. And then ... will you decide whether to separate or stay together depending on the outcome of that? What do you want from the counselling? For him to stop drinking?
I suspect that one reason he is behaving like this is because the situation is not clear. That's not surprising. It sounds like you acted quickly, because things came to a head for you. But the situation is blurry.
(The other reason, I think, he;s acting like this is just ongoing selfish immaturity and drinking.)
I think your first step is to decide what you want. how long do you want him to move out for? When do you want counselling to start? How much of a financial contribution do you want him to make? And when? How much contact with the kids do you want him to have?
Maybe you need to approach it as a separation and begin with a visit to the CAB?