Committed relationship roller coaster ending

I was in a committed lesbian relationship for 3 and a half years- my first actual relationship ever. We were very close friends in college and it turned into something more for her early in our freshmen year. I developed feelings for her in our senior year but refused to admit it because I identify as heterosexual. Finally, about three months after we graduated, I couldn't deny it anymore and two months later we became official. We live 4 and a half hours apart but were always in close contact and took every opportunity to see each other. We talked online whenever we couldn't on the phone. I would occasionally receive facebook messages that she had sent to other people through some weird facebook glitch. Well, about a week ago I received a message to another person in which she basically said some really inappropriate things concerning her feelings (even differentiating between friendship love and what she felt), her connection with this person (how she had never had a connection like that with anyone and never would again), and how it hurt that this person did not return her feelings. I believe this is cheating. She first told me she was asking advice from a friend after someone had professed their feelings for her. I did something terrible because I didn't believe her and I figured out her facebook password (not hard since she had all but told me before). I found the message in its entirety and confronted her. She then told me that she would tell me the truth. She said this person was someone who she had developed feelings for at around the same time she began developing feelings for me when we were in college. They had reconnected and she felt that this person had feelings for her so she was trying to let her down easy. She asked me why we couldn't just work it out, told me that I owed her that much given all that we had been through, threatened legal action for me figuring out her facebook password, and even threatened suicide. My father cheated on my mother repeatedly and I made it very clear when we began that cheating was my deal breaker. I wrestled for days with the urge to forgive her and break the promise I had made to myself the last time my mom took my dad back after he cheated. I needed some time alone to think and told her I need some time alone but she continued to text/contact me. Then, after another day of heated discussion, she told me she sent the messages on purpose. She told me that she did it to see how committed I was to us since I was always evasive about moving away with her. I have not been able to move away with her like we both want because I am the sole income earner in my household and am responsible for my mom and brothers. She told me I failed her test and that I clearly never loved her the way I said I did. The problem is that I do still love her. I feel like this relationship is unstable and cannot be saved though. There is clearly no trust. Should I walk away?

Wow, that's quite a roller coaster of a relationship! I'm not sure if my advice will be of any help, but any how I will give it to you. It sounds to me like your gf is not happy with herself, and so is/has pushed her insecurities onto you, which of course is not fair. You made it clear that you have strong feelings towards being unfaithful in a relationship and any/every relationship requires trust to be successful! There's no doubt you too have a lot of strain on your relationship, but life is full of problems-shit, you should both be complimenting eachothers traites amd working past it getting stronger. If she feels the need to 'test' you in such ways, I would propose she lacks trust? And therefor this is a waste of your time. I hope you sort it out, whatever the outcome just be happy. Sincerely, Charlotte.