Cutting out drinking completely is easier than trying to drink "moderately." One thing that helps is to view what you're doing now as practice, not failure. When you're learning something, you make mistakes (because you're still learning, not because the lesson is a failure), and you are learning not to drink.
Not having alcohol in the house is a good step. Having an alternative at hand — I make tea, a mix of shredded hibiscus and green tea and drink that — is helpful. I strongly recommend the book Changing for Good, by Prochaska et al. (https://www.abebooks.com/servlet/SearchResults?sts=t&an=Proc...) They found that changes of this sort (quitting smoking is another example) is a 6-stage process, and at each stage certain tasks must be completed to move on successfully to the next stage. If some tasks are skipped, the result is that the change doesn't take.
One thing to keep in mind: any amount of alcohol is harmful to health. Some studies found that those who drank a small amount (say, a glass of wine a day) had better health outcomes (e.g., lower all-cause mortality) than those who did not drink at all, and that gave rise to the idea that a little alcohol is more healthy than no alcohol.
However, this finding was due to bad study design: the "no-alcohol" group in those studies included both people who never had used alcohol and also people who had to quit because of health reasons. (This became evident when, for example, some in the "no-alcohol" group died of cirrhosis of the liver.) Once the studies were rerun, restricting the "no-alcohol" group to those who never drank, the illusory benefits of a little alcohol vanished, and the relationship between alcohol and bad health outcomes was clearly a direct relation: the more, the worse; the less, the better. Period.
AA has now been found to be effective, and you might try that. The benefit is that you have someone to talk to when you get the impulse to drink (and it's free). My own abstinence from alcohol came about gradually and indirectly as I worked on getting control of my budget (in part by focusing intensely on staying within my weekly budget after setting aside the money I'd eventually need for periodic expenses — alcohol is relatively expensive, so I stopped buying it, and after a while I didn't miss it, and then I realized I really didn't like its effects).