Is it okay to accept that your girlfriend told your secret when you had told her in confidence if the common friend is a co-worker?

No, it is not OK!!! You told her something in confidence and it was between her and you. She broke the rule of trust. Let her know you aren't happy about it. In all my years I haven't broken a trust issue between anyone, and consider it a priviledge that they would choose me to share their secret(s). The only reason I may break it is to save someone's life, but nothing else could pull that info out of me. If I was a creep, I could easily write a book and blackmail some very important people. LOL I would never do that. Read her the riot act! Tell her if you can't trust the person you love, then the relationship is on a downward spiral. Give her a second chance. Good luck Marcy