When she ignored me (and just tried to hide the ongoing contact better) I threatened to move out and told her she was placing me in an untenable position. She told me that my response was unreasonable - that I am a bad person for threatening to abandon her and our children.
Tell her that you won't live in an open marriage, that she's damaging the marriage with her behaviour, and that if your boundaries are crossed, she'll need to move out. Help her pack...
