I wouldn't mention the alcohol issue. When sharing with someone you don't know on a personal basis you have no idea what their biases are. Your employer might be hugely empathetic to your situation. On the flip-side maybe their spouse is an alcoholic or their ex-spouse or one or both parents and they hold a lot of anger about it. Maybe they think alcoholics are - who knows what and would question why you hooked up with one, perhaps they don't understand alcoholism at all (lots of people don't and why would they?)
Now, of course I'm not saying any of the above is true, just that you don't know what their history is at all so you are just putting yourself at risk for no reason.
I would just explain that you really need to stick with XYZ schedule if at all possible, as you originally agreed to, as you do have a child (which I'm sure they are aware of). If pressed, then I you might mention there are medical reasons with relation to your spouse that you need to be at home at the times planned.