This is one of the reasons that I eventually stayed in my marriage -- I KNEW I would not be able to follow through with ending it.
In the very early days, we would go back and forth... back and forth. I'd kick him out, then take him back. I simply wasn't strong enough (or well enough) to follow through with the final decision. I loved him... in spite of the drinking.
This back and forth business was not working, nor was it healthy. It was a complete waste of time and energy. So... I put the decision on the back burner, got help for myself and found ways that I COULD stay in the marriage until I finally got strong enough to end it. To my surprise, I ended up finding a way to live with it. It was never my intention -- it just turned out that way. Today, he is working on his sobriety.
There have been some dark and hopeless times, but all in all, I've been pretty happy... in spite of the drinking. It was made easier for me, because my AH was not verbally or physically abusive -- he was a very functioning alcoholic (kept his job, did the chores/yard work). Everyone's situation is different, and only YOU can decide what's best for you.
I'm really sorry for your pain and know exactly how you feel. That final step is a doozie. I was never strong enough to take it. By the time I was, I no longer wanted to.