Well, to answer your question, yes, it is a dealbreaker if she were to actually do this. It is way too blatant a disrespect for me to handle, especially after all I feel I've agreed to let her do (probably more than 99.9% of men on the planet would agree to).
If she continues to press this, I will probably speak with her guy. We had an understanding that we would never do anything that would make each other uncomfortable. I feel he'll agree, because he knows firsthand what can happen when open relationships go bad.