AA is set up to offer a HUGE amount of support for alcoholics. He is still an alcoholic, he will never not be, even if he never touches a drop again and does ago of the hard work successfully. He cannot, ever, have a healthy relationship with alcohol, period, that's not being mean, that's physically proven scientific fact.
He needs to go and talk to his AA sponsor. And get himself back to an AA group, regularly. And access any of the wide number of support options there are available for alcoholics. If he honestly thinks he can drink again without having a detrimental impact on you and his children, it won't hurt him to have made that decision rationally, having got himself fully informed from AA and addiction experts, now will it? (Spoiler alert, none of them are going to tell him it's a good idea).
My friend's ex started drinking again. He'd done it on and off a few times. He wad picking their 5 year old up from school one day, and she happened to have gone to school to speak to them about their son, and she saw his car... with an open pack of beers in the back, and an open one in the driver drinks holder. Thank God she was there. She took her kid home in her car, and now he's lost the freedom to see his kid without one of his parents or her there, and he can't be trusted to be drive his son anywhere. He is otherwise a bloomin amazing parent, fully engaged even though they are divorced, but the drink told him it was okay to go to school to pick his son up while drunk... and that's somebody who thinks he has a normal relationship with alcohol now.
Your chap also needs to see his GP and a mental health charity about other options to help him relax in the evenings/deal with depression. Again, if he is being reasonable and rational, it won't hurt and could likely help to explore all the options for relaxation in the evenings. You probably won't be surprised to hear that drinking alcohol to relax/recover from mental health is almost never recommended
and certainly not to a person who has (even in the hypotherical past tense, everything's fine now) had alcohol problems.
And if he isn't being reasonable and rational, well, I feel sorry for him, because he really is going to learn (or not) the hard way. You can't put yourself or your kids in the way of harm.
You sound like you're doing really well with this, OP. I'm sad to hear he thinks your joking. That alone makes me suspect maybe he is already back on the booze;'it certainly indicates he hadn't given it the soul searching thinking that he needs to have done.
Best of luck. Stay strong.