If my DH was getting this anxious, I think I would come home earlier.
With all due respect, Pickle, you have clearly never lived with someone with anxiety and depression. It controls so much of your every day life that it is very difficult to allow it to control your personal free time too. A person needs a bit of space to spread their wings and be themselves. Even if that is just to go out and have a few beers.
Smiley
If you have depression and associated anxiety, then it's possible that he really does need the freedom from that that a night out and a bit of a blow out on the beer, might provide.
If it were me, I'd wait until there is time and space to discuss it. I'd talk about how the way things are currently working isn't meeting either of your needs. Because, actually, the more you phone him up whilst he's out and give him a hard time, the less he's going to want to end his fun and come home and the more you're going to give him a hard time... it's a vicious circle.
Getting so drunk he can't find the toilet or care for the children the next day isn't good, but if he is out having a good time with his friends and he knows that you are still up, getting stressed and angry with him and he knows you were going to have a go at him when he gets in, I can see why he might have another beer and stay out another half hour. If he's going to get grief anyway, he might as well feel like he deserves it.
You need to find ways to manage your anxiety and resulting behaviours and he needs to commit to enjoying himself in a more reasonable way, which might happen if he doesn't feel he's walking back into an attitude.