Should I trust my girlfriend to do the right thing?

You can't change her. You can only change the way you handle your behavior in response to hers. She probably is too nice and very naive, and so these are things you will have to continue to deal with until she gets the picture, if she ever does get the picture. People that sweet and innocent tend to keep wearing those rose-tinted glasses when they view the world and that is in some ways very appealing. You get the good with the bad. It also means she may get herself into sticky situations. And you will be there to pick up the pieces, if you want to be with her. Yes, trust her. Be wary of the rest. Don't give her any reasons to accuse you of being jealous. Jealousy isn't tied to her listening to you or not listening to you. Jealousy is tied to insecurity. That's your issue to work on. Good luck.