My girlfriend/fiance confronted me in much the same way that you have confronted your boyrfriend. That was December 7, 2015 and I haven't drank since.
But, I can tell you that your boyfriend needs to quit for himself. It doesn't hurt that perhaps you gave him the final push to seek recovery, but if he is quitting to appease you or keep you or get you off his back, it will not stick. He faces a difficult road and if quitting for himself is not his highest priority there is only a very small chance of success.
I'll say this - you need to take care of yourself and your kids. Make that your highest priority. Let your boyfriend deal with his own issues and have a plan in place for getting the hell out of that relationship. It is imperative that you come to understand that you didn't sign up for a lifetime of hell with this dude, no matter how wonderful he otherwise is. And living with an active alcoholic will be complete and total hell.
As far as your own drinking, my fiance still drinks. But she is a "normie." I'd suggest that you put it down for a few months and then make the decision as to whether to drink down the road. If you have your own issues with alcohol, then you need to address those.
I think early on in sobriety it was best for me to not be around anyone drinking, but now I don't have any problem with it. My fiance quite often has a glass of wine or a beer when we go out. Others have different views, but now that I am well into recovery, I find it a bit offensive when someone decides not to drink as some sort of gesture of support to me. It's as if they are suggesting that I am so on the edge that their having a drink is suddenly going to cause me to rip the beer from their cold, clammy hands and chug it. I know they have better reasons for doing this, but I just don't like it and I make sure to make my personal views on the issue clear to those that are close to me.
Good luck!