I'm guessing on some level you already know this, but it means you're up the creek.
Open relationships are fine for some people, but honestly, for most people they don't work. One person or the other agrees to it to try and hang on to their relationship, and can't handle it when another person enters the equation. You're experiencing the classic problem, unfortunately.
Ask yourself if an open relationship is what you really want. If it isn't, then you need to break up with her. That simple.
As a non-monogamist I'd liked to weigh in here.
He lives in another state. She very well could like him a whole lot but the distance sucks ass. Are you her primary partner? Do you know how she feels about you? Are you both clear on your own relationship?
She could very well feel torn about this guy because of the distance. At least that's how I know I feel. I have some secondary partners who live far away whom I care about a lot and would like to see more often but the distance makes that difficult. So she could be weighing it in her mind whether or not this is something worth perusing. Hence why she doesn't know how she feels. Yet.
That does not mean you are up shits creek. And RF, a lot of these relationships don't work out because of lack of basic communication and stating how we feel about the people we are with. I have a primary and he knows exactly where he stands and he knows exactly where my other partners stand in how I feel about them and what our relationships are. I get the same courtesy from him. He has one other secondary that he doesn't see often because she lives two states away. He sees her when he goes home to visit his parents. I know how he feels about her. Consent and communication is what makes these relationships, like any other relationship, work or crumble.
Yeah, I think this is a case of a guy who thinks he's okay with an open relationship but actually isn't. Completely understand, of course; I could never handle the hassles of an open relationship. I'm also too selfish to accept anything but complete monogamy. :/