You crossed a line.

Your girlfriend has a right IMHO to be upset.

Let your girlfriend have time alone. If you push her for contact she could end things for good.

Your girlfriend being friends/not being friends with this other girl isn't so much the point. I have a feeling your girlfriend may know this girls true nature and doesn't want her messing up your relationship. We women have a way of knowing this about one another while guys are oblivious to the fact that some women have no class and have no problems crossing the line, making friends with another woman's man and then stealing him.

As for trust, you may never get that back. It's one of those live and learn kind of things. You can't buy her trust. You will have to prove you are trustworthy over time.