You met her very recently and she was quick to move in - do you even know if she moved in with you out of want or simply because she needed to go *somewhere*? I'm sorry; I don't know the girl in question but here it is not even April yet and you've been with her not even two months. She is now moving in with a 3rd fella in this short span of time. What a great way to never have to pay rent! I give you X amount of sex and affection and you give me a place to live. We have a term for this don't we?
It would be very difficult to feel an emotional connection with someone that busy. Your jealousy might just stem from that and not because of some real struggle you have in connecting with people.
Just like in the monogamy circle, you're going to find people with a lack of rational thought and integrity. Do you even know this girl well enough to say anything about her character for sure? Poly doesn't mean anyone willing will be a good partner to have.