Lie detectors tests can be deceiving, especially if you and her have different beliefs about what "cheating" is. If she honestly believes something, then it will not show in the test. I think the real issue here is that you are even considering putting your wife through a lie detector test.
If you can't trust each other enough to figure this out through conversation, I think you may need to go ahead and move on.
You have left so many questions that it is hard to give you an answer. Perhaps you should re-post with more detail.
Get her and him in a room together, calmly and quietly talk to them both - how this is affecting the entire family, and simply ask them to be truthful. I would watch each of them and their reactions; responses - and I wouldn't make it public knowledge, rather, take the information and think about whether this was a one time event; based on some kind of other issue, etc. If they are not up to this as two, purportedly, decent people? Then go ahead, for $1,000+ bucks (what a frickin waste of good money) let her put her "money" where "her mouth is" so to speak, and take the test... Pitiful...Seriously...That trust has been shattered...The fact your intuition has always told you ("felt") that there might be something between them, may very well be true...I think it's time to be big boys and girls in this instance...Time to be truthful...Many lives seems to depend on it to some degree...Certainly?
Your peace of mind...She owes you, at the very least? The TRUTH. Goodluck dear, very painful and I am, so sorry... Grace.
Think if she suggested a lie detector test shes telling the truth.
You asked her to tell you the truth, now you need to decide if you want to stay and trust her. Without trust you have nothing. And you need to stop bringing this up.
And move forward.
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.