I'll add my couple of cents in the mix (just cause I can
Firstly, I don't think you should exert any "control" over the situation. You have nothing to control. You have no "right" or no "claim" to this girl. She is a person, free to live her life and make her own choices. That being said, you do have a right to your own feelings and opinions. The only option you have is to share your feelings on the issue with her and let her make up her own mind on the issue. You should not pressure her into any decision, or force her to do something, that is not your place.
Now, one of the major issues I see here (and where it seems like the problem is arising) is from this girl not telling her friends about her relationship. See, if she just said "I'm involved with someone" this whole mess would not exist.
As to what to do or what happens next? Well that is all up to her, all you can do is tell her how you feel.
Good luck.