I think it's clear that you are beating your head against a wall. I actually think it is unfair to believe that she will never get sober, or cannot be drink-free for more than 3 days. I know for me, hauling out the crystal ball never did any good.
I think the very most important thing here is the child. Don't know how old, but if she is a minor, please do what you must to keep her safe. That's your job.
Your wife will either get sober or will not. If any of us hundreds of people on this board knew how to get our loved one sober, we'd be zillionaires.
She is not in recovery, she is an active alcoholic who isn't even motivated to try and cover her tracks.
Please also try and take care of yourself. This can make us almost as ill as the addict.