Times when you stopped drinking, did you do it alone? With no help? Did you work on yourself with a therapist or group? Having a support system can greatly improve your chances of success going forward.
A new baby is stressful. You hired a prostitute. I would imagine you feel neglected by your wife. The thing is, this is the new norm. You are no longer the most important thing in your world. You need to put others first from now on. This is the bargin you agreed to when you created a new life.
I have been exactly in your situation. You need to work on yourself, hard work, just stopping drinking won't address the empty place you feel. The place that prostitute filled. The hole the drinking fills. Being disgusted in yourself only goes so far. Loving yourself is so much better.
Get some sober folks around you, get a support system. Parenthood and marriage are hard work.