Well, I have a couple of thoughts.
First of all, she's an alcoholic. And "functioning" is a stage, not a kind -- meaning without sobriety, she will go from "functioning" to "not functioning" eventually.
While I don't think this is quite right:
my counselor and everyone I speak to says the affair was because of the drink
I do think they have a point here:
unless that stops, it doesn't matter what else we talk about the lies will always be there.
Alcohol clouds judgment, for sure. But a person who would cheat on you drunk would cheat on you sober -- in my book, blaming your behavior on being drunk or being a drunk doesn't cut it. Hopefully, she wasn't drunk at work when she was kissing her boss?
What I learned from being married to an A, and what i still practice in my life, is that I can only control ME. People around me simply aren't in my power to control. I think in a situation like yours, you could decide that you are going to ignore the emotional affair for now and focus on her drinking and how that affects you. Or you could say "I don't want to be married to a person I don't trust, and she is showing unwillingness to quit the job where she's around this guy all the time. I either have to decide to trust her, or not. If I choose not to trust her -- well, then it's up to me if I want to stay married to her or not."
See how that is different than "I need you to quit your job"?
You are taking responsibility for your feelings around the whole mess -- you're not telling her to change, you're telling her what YOU need in order to be able to trust her/stay married to her.
You could do the same thing with her drinking. Rather than trying to get her to quit, you could decide what you want out of your life. And present her with that. That's what I did. I told AXH that I was not willing to spend my life married to an alcoholic, and that if he chose to continue refusing to get help, I would leave him. That wasn't a threat -- it was a boundary. Here's what I need. Here's what I would need from you in order to stay married.