So I told her she needs to show me something before we can go. Not necessarily move back in but something along the lines of kicking this guy out of her apartment. Something to show me that this isn't some sort of "feel good" for her conscience.
I think youre on the right track, but the logic in your head is a little turned around. See, your focus should be on what YOU need - not what SHE needs to do. For example, saying things to her like "Im not willing to go out with someone that is in a relationship with another person." Then it becomes about what your needs are as opposed to controlling certain aspects of what she does.
Id recommend reading the boundary thread for more (and frankly, better) insight.