OP, I'm the one with the alcohol addiction in our family. I didn't lose my children, or my husband, but in conversations we have had, it has become clear that the possibility entered my husband's head more than one. And fair enough too. In all honesty, I think that at some points my children would have been a lot better off, and that they possibly direct anger at my husband for not shielding them/putting them first, that should be directed at me for what I put them through.
We cannot have one drink. When you say 'for him, one drink is too many', that is because he knows, because he has seen, so often, so BLOODY often, that for YOU, one drink is too many - because you cannot be trusted, or trust yourself, to stop at one. In all probability, one will become two, two will become three. . . and whaddya know, you're all in a horrible situation of you and alcohol's getting together's making again.
I have been sober for over a year now. One of the biggest things that stops me is the sheer horror I know that my youngest, in particular, would feel, if she saw me take 'just one drink' again. Because it's not just the reality, it's the possibility.
It's a bit like earthquakes. You don't know if it's going to remain just a gentle 3.5, or whether it's going to turn into a life altering 7.3. And so, the possibility, as much as the reality, does the damage.
You cannot rely on 'getting the right help' to 'fix' your addiction. It can't be fixed. It is a life time condition that you will need to actively manage. And no one, and nothing, is going to fix it for you. Ultimately it comes down to you, finding the ways that work for you (that is where the help comes in) to stop yourself, every hour of every day, thinking that you can have 'just one drink', and then having that one drink, that turns into many.