I had the same kind of father you had growing up. When he died I was 29, I actually felt relief at his death because he went through years of getting sober, falling off the wagon, getting sober, falling back to drinking. He was a very kind man when sober and a SOB when drunk. I know what it was like not having the kind of father I wanted.
Certainly your fears are understandable but you have it within your power to become the father you want to be. The therapy can help you heal some of your anxiety (PTSD?) about your past, and hopefully you'll follow through with it to grow and heal, and allow yourself to become awesome. It sounds like you have the heart and soul of a great father in the making.