Why would she trust that you are just going to taper down? What has your recent behavior shown her about how you drink?
Anyway, if you can't go to a doctor and get proper meds, then you probably need to taper. So let your wife leave and taper down and stop drinking that sh!t. Once you are finally off the alcohol re approach your wife.
You've tried drinking and that doesn't work. How about AA? Or Rational Recovery, SMART, therapy, Allan Carr's Easy Way... Or maybe just stop drinking alcohol no matter what. I don't have an answer for you, but from where I sit, continued drinking seems a poor choice.
Nothing else will matter if you die from withdrawal, so I'd work on that first.