If it was anyone but her, I'd say you were right. BUT... this woman is a grade A nutcase. This would not stop her. She is so into her own personality disorder that it would make her more determined.
Um, I was referring to your wayward husband. Your boundaries need to be established with him, as you are choosing to live with him and try to remain friends with him. Healthy boundaries will be important during such an effort, and this (saying "ILY" to his affair partner in your presence) is simply beyond the pale.