I'm sorry I was a little harsh or blunt before, but I have read a lot here and this stuff is fairly predictable. The other man being a co-worker was easy to figure out for the nature of the affair and the way she tried to cover up.
You are dealing with maybe your first infidelity but I and many others here have read hundreds, and like I said, it is all so predictable.
Cheaters generally will take whatever you give them. It was not just sex, she is deep, deep in love with this guy. This is her behavior, her actions, you might as well just ignore her words, those are so easy to lie. Crying is so easy to fake, never let that affect you or make it seem she is being truthful because of her crying. It means nothing, or it means something nothing to do with you, maybe it is about her crying about her, or her other man. Just focus on her behavior and actions.
She'll have to leave that job. How will you be able to stay married and stay sane knowing the man she is in love with and has sex with are seeing her whenever she wants? Why would you even want to try?
You did good tonight, you made real progress, but now you might be having a setback tomorrow. You shouldn't let her be with toxic friends who are not friends of your marriage. There are three camps - friends of the marriage, not friends of the marriage, and neutral. She should stay away of people who are not friends of the marriage.
It is better to keep her home with you than with the toxic friend. The toxic friend will give her a pep talk on "keep cheating, you deserve to be happy, and OM makes you happy." Trust me, this is how it goes. So add that to the list she's got to get rid of, the job, and the toxic friend. Both a fight for another day, but tell her to come back or to stay with a relative tomorrow night.
Just because she "agreed" not to have sex with other man, doesn't mean she will actually live up to the agreement. She is in love with the guy and she is hot and bothered for him, too. Even if she truly intends to not have sex, she might fall to temptation if he pushes her. The sooner you can tell other man's wife, the better. Having other man throw your wife under the bus really helps dampen her desire and love for him. That is job 1 for you right now, tell other man's wife.
Job 2, get a voice-activated recorder in her car. Despite her "agreements," this affair is not ending easily. Like you said, only a couple days ago she was telling you she would flaunt the affair. If a cheater doesn't go all in to the marriage immediately upon being confronted about the affair, then it usually has some level of affair going underground. It is almost certainly it will continue with your wife because of her still recalcitrance on being "all in" to your marriage.
She still is in camp of other man, she is just placating you with easy words until she can figure out how she can keep her soulmate other man. She is having a war strategy tonight with her toxic friend of how to go forward.
Besides a voice-activated recorder in her car, get one for your person. Record it when she talks to you, on phone or in person. Toxic friend was divorced, she may know some tricks, like falsely accusing on domestic violence to get you out of the house. If nothing happens, it is a small inconvenience of recording it. If something does happen, it saves you months or maybe years of frustration dealing with a false accusation. Don't underestimate the influence of toxic friends.
Consider the toxic friend as an extension of your wife's own character. Why would your wife want to be friends with a toxic person who thinks cheating is a good idea? Doesn't this make you think that your wife has the same outlook as her friend on the subject of cheating?
Tell the other man's wife. Put a VAR in her car, and one on your body.
After that, you'll need to get her have STD testing, get her out of that job, get rid of toxic friends, get her a polygraph.
After that, you can work on your marriage.