The cheating doesn't stop, no matter what the alcoholic tells you. Look at yourself very honestly. Your relationship doesn't really have much to do with true love, but with co-dependency and addiction. You can't save her, but you may be able to save your children ... and maybe yourself. Protect yourself, too, from the inevitable STDs.
Don't mean to be harsh, but my family has paid an extremely high price for my willingness to believe the lies. If I could spare anyone, I would.