The thought of an affair had crossed my mind. What I don’t understand is that she has been hurt in the past from a previous partner cheating on her, why is she is having and affair? She knows how painful it is.
Welcome to MB.
It looks very much as if your wife has recently met someone and is in an affair. It's likely that the separate therapy was not aimed at building your marriage, in the way that the Marriage Builders programme is aimed. In her therapy sessions she was encouraged to explore what was making her unhappy, and to extricate herself from the unhappiness - and the source of her unhappiness was identified as being her marriage. Individual therapists usually do not care whether marriage as a way of life is better for individuals, their children, and society as a whole, and so if the marriage is seen to making the person unhappy, the solution is to get out of it.
In other words, her therapy gave her the means to coax you gently into accepting the breakdown of your marriage. First it was pitched as a trial separation that would be good for both of you and allow both of you to think and breathe, and then, after a suitable period of time, the goal is now to persuade you that you are better off separated and the marriage should end. The therapist might not even know that your wife is having an affair, and if he/she does know, they might well argue that this is irrelevant to the breakdown of the marriage. For your wife, therapy is the best thing that could have happened to her affair.
The problem now is that you have been persuaded to move out. I don't know the legalities of the "nesting" arrangement and whether this allows you to move back in at will. I can see your wife using legal means to get you out of the house if you simply did not leave after your next visit. I think you should seek urgent advice from a lawyer about your rights in that matter.
Your having separated also affects the legalities of spying on her. If you can't get hold of her phone, normally you could still install a listening device into your own bedroom and your own car, if it is shared, and a keylogging device onto your own PC or laptop that she might use. We've had many a spouse find exactly what they need without getting hold of a phone. However, you need to make sure that any spyware that you install is onto devices that are just as much yours as hers.
The best thing, though would be to instruct a private investigator, and he or she would probably get evidence of an affair within a day, since your wife is separated from you and feels free to do what she wants. She probably meets her new man on her weeks off as well as at your house on her weeks at home.
In other words, you'll need to be pro-active and work quickly to find evidence of the affair she is undoubtedly having. After that, your goal would be to expose it (with guidance from us), but I don't hold out a lot of hope, I'm sorry to say, since arguably you accepted the end of the marriage by moving out.
Where does she stay on her week away from the house?