How do you know if a girl is trustworthy and want to be in a real relationship?

my ex we were dating for about a year, and we broke up because she is moving with her dad. Her dad is like a government official and he won't approve of me dating her, that's what she said.. Although, her mom thinks he will, if he thinks about it.. At first she didn't want to try, because she already thought he would say no. However, i felt like she didn't want us to stay together and wasn't sure.. First, she told me her secret that she couldn't trust me completely, but it was understandable, because we are far apart at the moment. But i was going to see her this summer, and he is stopping me from doing that.. But it hurt when she told me that, because i trust her, most of the time. She is a model, and i feel like i could loose her at any second to a guy better or worse than me. That's why i want to be my best with her and don't loose her! Yes, you could think this is petty love, but it's more than that to me and i would rather keep it than throw it away. I don't like thinking what could've been.. Now we are single, and i am not looking for any girl and she say she is not looking for any other guy, and that she is still in love with me. But it feels like a lie, and i don't know why.. We don't trust each other and at the moment that is really bothering me.. If we see each other all of this will be fixed, but i'm still not sure.. I would like to hear someone's advice and just words of encouragement. I want to give a example of how i feel and i need tips. Could you help me please?