hi smetz. Well there are a few things going on here. This first is that he doesn't have a problem with his drinking, you do. That doesn't mean either of you are wrong or right, it just is.
You told him that if he continues to drink, you are not going to stay, but you didn't actually follow that up with any action, so you didn't really mean it, it was more of a threat than a boundary? Unless you are willing to back up a boundary you make, it's really kind of not worth saying. It also indicates to the other person that you don't say what you mean, that they can stomp on your boundary and there is no consequence.
Is it two or three shots a day? He's lying to you so you have no way of knowing.
That's really beside the point though. It is completely up to you what you want to live with. Are you willing to live with a drinker? If not, then you can choose to leave. Again, he doesn't have a problem with his drinking, so anything you say is probably not having any impact on him.
As for following him or looking at his phone or however you found out, well now you know. It will be a trust issue for him I suppose, but you already knew that maybe?
If he is going to fall off the wagon (well, he already has), that's out of your control. You didn't Cause it, can't Control it and can't Cure it (the 3 c's). No matter how much you care, no matter how much love you have for him, if he is going to drink, well he is. He is a grown man and does get to make that decision. Your decision is, do you want you and your children to be around that?