Fof2,
Turtle just gave you some fantastic advice.
The order of doing things is very important. Write and send the exposure letter. Make sure all that count know of her affair.
She will be mad as heck. She will threaten. She may leave, but she won't leave her job will she?

Let this percolate around for a week or so.
The issue is that for recovery to happen, she MUST have no contact. She isn't really committed to recovery. I think as do others here she will play at recovery, then some months later terminate the marriage saying "I tried, it really wasn't the affair I had, but just that good old Fof2 is just not my type of man."
YOu expose, you prepare for plan B, when recovery is mentioned you make darned sure that NC is part of it, and that means someone leaves that job. Do you see any room for negotiation at this point? I sure don't.
She is only negotiating her affair with you now, because you caught her. You were not part of the conversation where she discussed bringing another man into your marriage, your family and her life. My guess you were not invited to that conversation. No negotiation on her part. There can be none with regard to your boundaries.
I have forgotten the age of your children, but if they are teenagers you need to sit down and have an honest discussion with them. Their life is being torn apart and they may not know why. It is time you stood up and showed them what kind of man you are, and that is not the type who allows his W to take other men into her life and body.
Expose the affair to everyone.
Weather the storm of her anger.
IF she doesn't leave, she probably won't as she loves her job and she has already soiled her nest, then discussion of recovery will come. That will include NC period.
This stuff is simple Fof2, it is just not easy.
God Bless,
JL