Just my two cents as someone who experienced both the alcohol use and infidelity in my relationship.
I don't know if they are connected in terms of his behavior, but both the alcohol use and the infidelity made me feel similar. I felt out of control, at fault, unlovable etc.
In both cases I thought it was somehow my job to make it all okay so it would never happen again.
I have learned that in both cases it is all on him to get better (and to even want to get better). The reason for the "unacceptable" behavior does not matter...the fact that is occurred does. I also should not reward someone for bad behavior or after bad behavior because he wanted something (in this case like coming home).
Al-Anon helped me with both types of recovery. As did my own individual counseling. Both of those could have been done regardless of if I was living with my qualifier or not. Honestly I probably got more out of it because I was living alone because I did not have to test my new skills on a person I had struggle to set boundaries with and be detached with before.