Awfulawfulday,
I am sorry you had need to go looking for this forum, but glad that you found it.
Unfortunately, there are no guaranteed one-size-fits-all answers when it comes to infidelity and reconciliation. It would be great if there were, but they just don't exist.
What you will find here is a lot of real-life experience, and thoughts based on it.
At the moment, you must be reeling. We all were. However, unless this is a 100% immediate deal-breaker for you - and I would guess it is not, because you are here and not already filing for divorce - I suggest you put your decision-making into neutral gear for the time being and (1) take care of yourself physically, and (2) see the coming weeks as a time for investigating and assessing the extent of your wife's issues.
Every relationship is a gamble; no-one gets married thinking, "This has disaster written all over it", and yet more than seventy thousand people have become members of this forum.
However, we can hedge our bets and make our gamble as informed as possible by doing as much research as we can. And that is what you need to do over the coming weeks.
I find it troubling that your wife has a history of drinking to the point where she would climb into a car with anyone. Not just for her safety - which is a major thing - but because it sounds like she has a history of doing it multiple times.
What she has done recently raises questions about what happened in past years when she went MIA. It would be comforting to think you have now been told everything, but I think it would be a mistake to believe that at this stage.
The fact that your wife initiated the sex means that you need to delve into those times when she went MIA further. I am sorry to say that, but if you are going to re-commit to being married to her, you really need to know what you are getting into, and what has gone before.
and also mentioned she drunkenly kissed another coworker previously(wow..)
If you had read a lot of the stories here, you would know that 'kissed' is sadly often a euphemism for something more. That does not mean it is 100% bound to be the same in your situation, but it does make alarm bells ring.
It seems that a lot of wayward spouses use 'kissed' as a catch-all for physical intimacy, or leave out the, "...and I also did x, y, and z" that could follow the statement, "I kissed a co-worker".
Many wayward spouses engage in a process called 'trickle truth' - often shortened to 'TT' in these forums - after their infidelity has been discovered. It is almost like the issuing of a series of press releases, beginning with a heavily redacted and sanitized version, and building steadily with each further statement.
I am not saying that to upset you, but to prepare you for what you may experience.
If you were going to divorce your wife immediately, with no interest in any further consideration, there would be no point to have her leave that job and workplace. However, if you are thinking of trying to reconcile with her, I think she definitely needs to get out of that job and being around those co-workers as soon as possible.
There are several reasons I say that.
1) If your wife has kissed one male co-worker there and slept with another twice, there is a fair chance that she has a reputation among the men there that she may or may not be aware of. Men love to talk about their conquests, and a woman who likes to drink a lot, and who has poor boundaries, sets herself up as a target for any low-life who wants to buy her a few drinks at a work event and see how far they get. For some of the guys there, she may be walking around with a target on her forehead. The problem is exacerbated if your wife actively pursues or initiates with them.
2) Leaving aside male bragging, other people there must be aware of what was going on. It is not hard to spot when people are 'close', and people love to gossip. It is quite possible that there is a toxic atmosphere in that workplace that condones or actively encourages affairs, which is not a good influence, and not 'friendly' to your marriage.
3) Any workplace can have after hours social events, and some can be 'safe', but many - particularly when booze flows - are not. If such events are a regular occurrence in your wife's present job, they pose an ongoing threat of a repeat performance, and they are clearly not safe for your wife to attend.
4) If it is possible for you to attend those get-togethers, and you are considering doing so to act as a guardian to your wife, then you may well encounter the two men you know your wife has been intimate with. That is a tough situation for any betrayed husband to be in, and often gets out of hand physically, or feels humiliating. It is far from an ideal situation, and not one I would recommend.
5) Although your wife could change jobs a dozen times and cheat in every one of them, if she is sincere about wanting to change and re-commit to the marriage, a new job where she has no baggage or history as a productive target for male co-workers to hit on would at least remove some of the issues mentioned above. It can be very hard to break out of a 'role' once people cast us in it, so a change would be easier to make in conjunction with a fresh start in a new job.
Getting therapy for myself. So I can focus on me for a while.
That is a very good thing, and I hope it is beneficial to you.
Your wife needs to get into individual counselling too, to discover her 'whys', and what her deeper motivations for cheating are. At present she may be in panic mode - aka 'damage control' or 'cover your ass' - saying she will do anything and everything to save the marriage, but only time will tell how committed she is to doing that forever more, rather than just a few weeks.
A question to ask when you feel ready is, "Why do you want to be married to me if you are actively pursuing other men? Are you as 'happy' in this marriage as you claim to be?"
Another one to ask her is, "Why should we stay married?"
Let her go away, think about it, and produce a list or a letter for you that contains her thoughts.
Her answers (both what they contain and do not contain) may be enlightening, and it sets up a dynamic that puts the onus on her to save the marriage after she fired some missiles at it.
It is not down to you to save the marriage; your job is to try and assess if your wife has what it takes to mean that staying with her will not be a mistake.
Your wife clearly has issues with booze and boundaries. Those are not small things, and they have impacted on the entirety of your relationship with her.
With commitment and sustained effort, those things can be changed, but it will need your wife to establish and permanently maintain a level of self-control and self-management that she has not demonstrated so far.
If she does not, then she will essentially be a ticking time-bomb, waiting for the next boozy smooch session at a work event in a year's time, five years' time, or ten years' time, after both of you have grown comfortable and complacent.
I think it is important to change some things about yourself too.
You now know that it was a mistake to accept your wife vanishing from the radar screen in terms of location and communication. That has to become a cast-iron deal-breaker in future for you. There must be no more, "Well, she gets a bit drunk and switches her phone off..." It is not safe for her, and it is definitely not safe for you.
Acceptance of her boozing needs to cease. She is not a 'safe' drunk, period.
If the co-worker she cheated with is married, or has a girlfriend, then she should be informed about what happened. Do not tell your wife you are doing that, or she may warn him, and he can tell his significant other that a nut-job is telling lies about him.
There is much more that could be said, but that can be done as your your thread develops.
A lot of people here are on your side, and want the best for you.