I think affairs and unfaithfulness are pretty common behaviour in active alcoholics, whether they are drinking at that moment or not. Drinking is a symptom of our sickness. I heard people talk of alcoholism as a spiritual malady, or an ego run riot, or having an alcoholic perspective. And those things made sense to me. The state of being restless, irritable and discontent led me to do some pretty bizarre seeking for relief. Sometimes that might be in a bar or a bottle. Others it would be more thrill seeking. Others it would be for that elusive thing or person that could make things feel better, and this search could easily turn a little insane.
Of course, I know nothing about your affair. But I do know that when, in the steps of AA, we do our inventories (that we share with our sponsor, not everyone or anyone in the rooms), one of them is the sex / relationship inventory. I've never heard of an alcoholic with nothing on that inventory. I also know that the steps have helped me to stop that insane scrabble for relief that was my life prior to recovery by guiding me as i worked / work on my perspective.
Things / relationships can and do get better if we work on our recoveries (through AA or by other means). Just stopping the drinking still doesn't address our spiritual malady though. We will be left being restless, irritable and discontent if we don't get busy with the business of recovering.