Welcome. I hope you keep reading here.
I haven't been in your situation as an adult, but I will give you my opinions from an alcoholic's perspective.
I think your control/punishment approach will make things worse for both of you, as it will likely cause resentments between both of you. Her resentment toward you will give her more fear and lead to her drinking more, not less. She may get very creative to conceal her drinking from you (booze in closets, luggage, the garage, car trunk, bushes, in the suntan lotion bottle). So, at first you think things are better.
Its a highly progressive disease that, left untreated, ultimately results in a horrible death. Drinking during the day and unchecked is a very bad sign. Then comes, shaky hands, jumpiness, insomnia, irrational fear of everything, bruises with no associated injury...and worse.
If you don't want to leave her, then you have try to get her to commit quitting, now. It's likely going to be ugly. Take her to the doctor and be brutally honest about her drinking.
Its no surprise she didn't like going to AA while she is still drinking. You could offer to go to open meetings with her, go to Al-anon yourself, educate her on what happens as the disease progresses. If that does not help, then you can go the intervention route and put her in a facility, or out patient program, for detox. Harsh, but its a harsh disease. You can't force her to stop, but if/once she is willing, you can help save her life.
As far as your question about when kids notice. Well my neighbor friends had an alcoholic Mom when we were kids (similar to your situation, un- or barely-employed mom, drinking daily). I figured out there was something wrong at about age 8 and that is was alcohol maybe a year or two after that. The kids will clue into it much faster if they hear you mention anything about it.
I hope this works out.