| | Re: Is she cheating?
... Or maybe they haven't.
Nonetheless, her behavior is inappropriate.
Tell her to end the contact with him. Then get into marriage counselling.
Why aren't you having sex with your wife?
If you do not think you will have sex with her in the future nor do you truly want to have a sexual relationship with her, be honest with her. Then let her decide if she wants to stay in a sexless marriage.