Like some others have said, I believe that when your wife promises she won't ever drink again she intends to keep that promise.
There were times I believe my AXH meant it when he said, "This time I'm done for good!". Sometimes he didn't mean it, he'd just be saying he'd quit to get me off his back. But other times, I could see the acknowledgement in his eyes, he knew things were bad, he knew he was hurting us both, I believe he wanted to change that... but he didn't want to do the hard work that would actually make that happen so it always failed. His demons always won. It was easier to pick up a drink then it was to delve into what was causing him to have the compulsion to self medicate in the first place. Us loving each other and our family was not enough to stop the crazy train of addiction and codependence.
I'm sorry this is happening to you, your wife and your family. I know exactly how painful, infuriating and defeating it is. I hope you take Dandy's advice to talk to a doctor about just how serious this is. It is not just as simple as never picking up another drink. If it were that easy none of us would be here. Knowledge is power, keeping seeking.