You don't necessarily need to word an "ultimatum" like "either you do this or else".
Just state what your personal boundary is to her. Something like "I understand you and I have things to work on in our marriage and I am more than willing to do so if you are. However, I will not be in an open marriage and have another man in our lives. If you cannot comply, then you will have to leave." this approach is different to what you're doing now, so you might as well try it.
Did both of you not want to separate or just her?
M-43 W-40 2D - 9 and 5
Emotion, yet peace. Ignorance, yet knowledge. Passion, yet serenity. Chaos, yet harmony. Death, yet a new life.