I don't think anyone has any business reading the texts on someone else's phone.

On the other hand, when she is with you, she has no business exchanging texts with other guys. She has a lot of control over who contacts her. If she stays in contact with guys wanting to date her, then, if I was you, I would say to her,"Let me know when you're truly free and available. I really don't want to date you, while you have other connections going on with single guys."