Vincent, if it was me, I would expect my girlfriend to tell the guy to backoff and not go to visit him. If she doesnt, I would seriously doubt my girlfriend's love for me. I would move on (i.e. break up) if she does not understand my feelings.
Put yourself in your girlfriend's shoes - would you do such a thing if you really love your partner?
Are you supporting your girlfriend financially? How old is she?
Cheers