Magellan,
Consider working with someone to develop a plan for when cravings kick in - something to DO rather than just sit there and mull it over in your head. Cravings just happen - if they didn't addiction would be a whole lot easier to live with!
So, since cravings always start with a thought, whenever you have the slightest inkling of a drink (or find yourself particularly irritable, tired or otherwise upset) put your plan into action. You might consider reaching out for help developing a plan - either via a therapist, support group or both. The problem with going it alone is that once you start down that path of "one or two won't hurt" the addicted part of your brain is talking pretty loud, and that's why it's so convincing.
Carl hit it on the head - this has nothing to do with willpower - willpower doesn't work as you have just experienced. If it did, then all of us would never have another drink once we made that first decision. Hang in there and consider finding a plan that is compatible for you.