Is there anything she CAN do to convince you that whoever said those words was just someone nearby and not another man (as in lover)?
To me it sounds like BOTH of you feel trapped in some unsolvable situation.
Based solely on what you share it sounds like you both are standing in opposite corners of the same room waiting for something to happen, without either of you really doing much to make anything happen and expecting the other to do exactly what you wish and want without either being clear on either.
Then occasionally you both might mutter something like "I could be somewhere else..."
Well... You COULD be somewhere else.
With or without her.
Why are you expecting her to arrange MC if it’s something you want?
Why MC? What do you expect an MC to do?
If you have doubts about the truth, why not ask her to take a poly? Simple question with a pass or fail result, with the failure leading to the foregone conclusion that you both decide this isn’t salvageable, but also with the lead-up time the ideal time to get the real truth out.
The reason the present is unsolvable IMHO is 100% your mutual attitude and stance. It’s not as if you want to reconcile, but more that you don’t want to divorce.
I think that if you truly want a shot at saving this marriage you need to get her on board with something like:
"What we have now isn’t sustainable. We aren’t working together to solve our issues. If you were with OM or some friends, you know aren’t friends of the marriage then I need to know. You are free to be with them if that’s what you want. You can also go for long walks if that’s what you want. But you also need to let me KNOW if you want THIS marriage.
I need to decide if I want this marriage, and frankly I don’t want it if I’m competing with another man. To save this marriage we both need to want to be here. Not enough that one wants it.
We can both be free to get what we want – if we are honest.
If you are willing to commit to me and I to you then that’s a start. We need to find ways to interact, rebuild trust and intimacy. We can get professional help on those aspects. But we can’t continue to try to do this in separate corners"
And then I would be ready with some suggestions on how you two can move on forwards – with or without each other.
"If, therefore, any be unhappy, let him remember that he is unhappy by reason of himself alone." Epictetus