Just a quick and not necessarily correct assessment:
His girlfriend is attempting to create a false reality to cope with her relationship, that much is clear. She is looking for something more than your hubby can give her but trying to capture it in little moments such as when you are not around.
She is struggling to find a way to be with your husband. She either really really loves him or is not ready to find someone that better suits the way she wants love expressed to her. My guess is she wants exclussivity. I doubt she is a "Cowgirl" but also doubt she is healthy at the moment.
She's going to have really confront what she wants from a serious relationship and express it.
You and your hubby really need to do the same. If he is going to be "open" poly and want to explore other women, he needs to be up front about that for her to make a solid decision. What he decides will affect you as well. The compromise that Redpepper has made to be with me has also impacted what she gets to experience with PN in many ways. You have to be prepared for that.
Good luck and stay true to yourself