Welcome to SR. Betrue.
I know where you are coming from.
I didn't think I was an alcoholic either, still don't as a matter of fact.
I quit when my wife gave me that one last chance and I decided that this time she was serious and I still think she is.
I wrote her a letter promising to never drink again or she can leave me for good and this was acceptable to her.
I read this letter almost every week and that along with a list of the negatives of drinking, which I read whenever I get that urge is enough to keep me from drinking.
It has been over a year and our marriage is stronger than it has ever been in 25 years.
It sounds like your wife wants things to work out and may give you yet another chance.
I also come here to SR for support and that has worked out well for me also.
You may need more support though.
I wish you all the best for you and your family.
Peace.