Hi (((Run)))........I am so sorry you are experiencing this pain.
My first husband cheated on me repeatedly. I NEVER trusted him after the first time.
We didn't receive any kind of marital counseling, so issues were never really dealt with.
So, decide if you both want to keep the marriage, then get counseling, so you both know how to work together on this.
However, if you feel you can NEVER trust her, it is best to part. Trust is the essential ingredient to a relationship as I have found.
My husband kept cheating and even with my best friend in the truth(tm). We divorced 3 weeks short of our 20th anniversary.
As I look back, I would have saved myself much emotional grief by divorcing him after the first time he cheated. (it was just before our 2nd anniversary)
Of course, this is an individual matter. I don't really know all of your circumstances and only you know what is best for you.
I am so sorry you are experiencing this....it hurts tremendously.
I second what Scully said about the alcohol issue.........it will make the matter worse.
Many hugs for you,