If you'll forgive me for saying so, your behavior sounds a little kooky. His friend was "too happy" for you? What does that mean? How happy is "too happy," anyway--you thought it was disingenuous? Then you confront her like some Teamster and tell her to stay away from your man--a man she has probably known longer than you have?
You're behaving like a bully, but she has been gracious and patient with you--a lot more patient than I would be. She assured you that they are just friends, and even offered to steer clear of him to make you feel less threatened. It certainly doesn't sound like she has any designs on your man. Wouldn't they be dating already if she did? Sorry, I'm on her side here. I think you have been unnecessarily aggressive with her.
I would do two things if I were you: one, apologize to her for acting like a crazy woman, and two, get a grip on your insecurity. It's not normal to be threatened by someone who's happy that you and your guy. Your relationship won't last long if you treat all his female friends this way. He will dump you before he dumps them.
Thanks for the question.