So sorry to read all this is happening for you. What a miserable time.
I would recommend that you try to segregate in your mind 'DH', the man you know he is and can be, the one capable of making you very happy, from the 'drinker' he has become. They are in essence two different men!
He needs to get to the nub of what makes him addiction prone, and if it's work, he needs to change his job.
He is clearly dependent on alcohol, and he will never be that good and stable man again until he gets help with alcohol (and possibly, he must also get help to reassess his depressive state and what causes it. It may be anxiety and stress rather than depression if it has a work cause. Thus, anti-deps may get him nowhere).
To some extent, arguing with him while he is in the grip of drink is pointless as you are not speaking to a rational man. Even if he is sober at times, he is an alcoholic who cannot see beyond alcohol just now. All his words and points of view come from needing and abusing alcohol.
I think you need to be cruel to be kind in this situation; ask him to leave the house until he has begun getting regular and sustained help with the drinking. He needs to live somewhere else. A man who is volatile in behaviour and is addictive cannot be around the kids.
Otherwise, you are the soft bed on which he falls whenever he wants to drink, and the only way to stop fighting with him over alcohol-fuelled topics is if he isn't present.
I would also say you need to speak to or write to his GP and make the GP aware that the anti-deps are being taken within an alcoholism context. This may bring a change to his prescription as he may not have been honest about how much or how often he drinks. While GPs cannot share info with you, it is perfectly reasonable to write a letter to his GP offering information in that letter. This does not breach their code of conduct or ethics since they are giving you nothing.
You mustn't feel bad about making him leave; he is unsafe to be around emotionally or physically while in this state of flux and addiction. Tell him you love him and have no intention to leave him but that he can only live with you when he can show evidence he's under a credible help programme and has been following it for at least six weeks.
He will throw back at you that he has agreed to counselling.
You need to stand firm and say that you need to see him in an active programme and committed to making progress before he returns since he isn't stable enough to be in the home with children present.
Just signing up for counselling is not enough as you previously made your boundary clear, and he has overstepped it. He must show he's attended it for X weeks and is making progress.
You can also validly agree that you have changed since being in your twenties! That is to be expected and is good; in our twenties, we have an undeveloped sense of self. Now, you know what is good and what is unhealthy. Your maturity helps you in life.
It would be very odd if you had not changed since you were half this age.