I'll put out there what I see as the reasons for a lawyer consult immediately. Again, this is NOT LEGAL ADVICE. Please consult a lawyer that you can retain for legal advice.
A person can talk with a lawyer and not have a case at all against another person or institution, at least in terms of monetary damages. Different lawyers may have different takes on any situation in terms of what can be recovered in a suit or if one is appropriate.
In this situation, it would be impossible to judge how this would play out based on the facts that have been shared, and I am not a specialist in this area of the law.
The danger here, as I see it, is the OM on several levels and the moves being made currently.
Professors go through sexual harassment training at universities and normally their codes of conduct would include that they should not be in romantic relationships with their grad students or the people that report to them. (The post MeToo era makes these situations more serious) This is true in all areas... almost all companies have rules regarding this type of relationship. Some require disclosure, some ban such relationships, some are more lax regarding these. Universities, at least for students, should have a Title IX office that at this point in time is far more active.
I don't need to say why these relationships are problematic. There's a tremendous power difference between professors and grad students; bosses and direct reports. In the case of grad students, the professor might actually control the trajectory of the grad student's career. They might be friends with those on a PHD committee, if that's an issue. They likely control grants for research. They likely can determine who is going to be a listed author on a paper. The power dynamic is profound. In a normal boss/employee relationship, it might be hard to escape such a thing in the case of sexual harassment, but doable. In this case, when his wife was younger, she would have a harder time escaping because the professional circle is so much smaller.
The MOST concerning aspect, at least to me, is that the OM hired, retained and reviewed the husband for years. How many career opportunities have been passed up because of this? Raises? Advancement? (i.e. possible damages) Think about how much of a control freak you need to be to employ your lover's husband.... that is sick in my mind. OM could have helped BS get another job hundreds of times prior in a higher paying position. In fact, wouldn't normal human behavior say that you would want your lover's husband anywhere but in the same office as you and WW? How easy would it have been to do this years ago?
Instead, OM wanted control over everything; keep everyone close and keep tabs on them. That's dangerous to an extreme.
If the OM is such a control freak without the moral resources to stop this arrangement, I doubt he only has only one affair partner. But that's beside the point. I hope there are not too many students that have to work with this guy.
The dangerous aspect here is that once the affair has been revealed the WW and OM will go into damage control mode. They are not focused on what is good for BS, but what is good for them. WW is likely scared for her career. OM is absolutely scared for his career. Neither know how this plays out, so they're scrambling to find a way to protect themselves as I see it.
What is clear from what BS posted is that they do not want the BS to continue working where he has been working.
They're using the carrot (higher paying job) and the stick (hostile work environment) to get this to happen. The danger is that they can do something profoundly underhanded to accomplish this result. Maybe they won't and maybe they will.
You NEED to talk to a lawyer because you're BLIND right now. You don't know the chess board at all and moves are being made around you. A lawyer will know how to play the game and protect you. No one else is interested in protecting you here that I can see.
It could be that the better job that gets offered to you is the best idea, but talk to a lawyer first about it BEFORE TAKING IT. Know what questions to ask and how to protect yourself.
The thing that makes this an emergency is when they used the phrase "hostile work environment" on the Zoom call. That's the worst red flag there is out there. You've worked there for years and there has never been a complaint such as that (I assume). But, say there is and that you're reprimanded or fired for it. Likewise, imagine that the OM and your WW might enlist the rumor mill to help with that. Some innocuous interaction years ago all of a sudden 'comes to light.' Maybe from someone else in the department completely unrelated to the situation, but still under the influence of the OM. What happens then? How easy do you think it will be to transition to another workplace that's at the same grade or higher with that on your record?
Say that you do nothing right now as you have been for a little while? It gives them time to lay groundwork. They may be scrubbing emails or communications. They may be gathering records. That time you took an hour lunch break but forgot to record it on your timesheet... maybe they're looking at it. The longer you wait on talking to an attorney the longer they could be laying groundwork to get you out.
Yes, it's better for them if you're employed. Yes, it's better for them if you're kept happy and keep your mouth shut about everything. But, and this is the ticket here, they don't care about you more than the problems you can create.
A lawyer consult will go over the actual issues that can have an impact on how to handle this situation. Likely, the advice will turn on things you probably have not thought about, your own jurisdiction, your own codes of conduct... etc.
As it stands now, I would be wary of taking whatever job is thrown at you by the professor. Think this way too... while the OM can throw you another job to shut up and keep his secret, what can the university through your way, and throw your WW way? A lawyer can tell you if it is better to go higher up the chain and say "OM and my wife have been having an affair for ten years, I no longer feel 'safe' in my department, I need to take some time off 'to determine what I need to do and if I can continue working there.'" Do you think the university has something better to offer you? It also puts them on notice about the situation. Talk to a lawyer before doing this. Please, I beg you.
It could be that the longer that you sit there, the more your possible claims could go away and the longer you accept what they throw at you.
Basically, they do not have your best interests at heart and you need someone that does. RIGHT NOW. It's not about your wife, your kids or anything else... it's about how you getting the right advice to be able to protect yourself. If a lawyer says to go for it, then do what you want to do. But, you don't know this game and they are clearly playing it. You need a lawyer to let you know IF you are being screwed by them.
Again, please just talk to one.
I expect the advice he or she will give you is to stop posting at least. If there is a way, just let us know you're ok and that you got counsel, but you should not post what the advice they gave you was, if they gave you advice. Always keep lawyer's advice between you and your lawyer.