I had to face your situation 3 times in my life, and drawing upon my experience, may be I can share some words of wisdom.
To trust or not to trust, is simply a state of mind — when we are relaxed, trust is always there. And Love too. What your gf does or does not will not matter at all if you live a stress free, relaxed life.
Also you should focus more on love and freedom and less on problems and insecurities. What you focus upon now will grow to reach new heights in future. What do you want? Love or Problems?
You cannot control your gf, even if you do, all happiness and love will flow out of your and her life. You love her, but you also love yourself, and for your own happiness it is important that you do not try to control, dominate and possess her. And when I say that I also mean its perfectly okay for her to sleep with other men. It will be difficult for you to accept this fact, but like I said, if you are deeply relaxed, it will happen naturally and by itself.
You still like your gf, so I would say give Love a chance, don’t kill it by thinking too much of problems and broken promises. At the same time also practice some relaxation exercises to burn out stress and problems. All the best 😀