You need to apologize to her... many times if need to. And let her have her own time to heal.
My Parents once did that to my sister.... but the boy was REALLY not a nice boy. And after that incident, she NEVER told them about any other crushes or boyfriends she had. So my parents never knew about her personal life after that. My sister NEVER forgot that, that her privacy was broken... and till this day, she remembers her privacy was disregarded. But she has forgiven them.
(I know for you, it has been 6 years since your incident happened. And your girl just told you she does not trust you after all that time. For my sister as well, it took MANY years for her to overcome it...)
Being a nice/good Mom & a person that everyone goes to for advice is one thing... but breaking a "confidence", for YOUR child, is a BIG deal. It's personal. So... it will take time. Lots of time. Ask your daughter HOW you can make it up to her.... over time. And maybe in time, she will overcome her distrust.
Your daughter sees you being so great with other people and THEIR problems, but for her, that is not the case. All she knows is that you "tattled" a secret of hers....and that she is the ONE person, that that should not have happened to, because she is your daughter. You are her Mom.
Tell her that you are very sorry, and that you made a "mistake" like many people do, and that even if you are a grown-up, we still are not perfect. Be open with her... don't force it though.... for a child, not being able to trust their Parent/Mom, is a really big thing... and they are sensitive about it.
The thing is, and I'm sure you know... it's not just about keeping confidences for your daughter... it is about building a relationship... and so that IF she is in any dangerous situations, that she WILL come and tell you, in the future.
Is your daughter open with your Husband? For me and my sister, my DAD was the one we went to with our 'confidences.' We just trusted him more, in a way, and he always understood us.
No matter what... there has to be at least ONE parent, a child can go to, with "secrets" or problems or concerns, or confidences, or worries, or stresses. Otherwise, both parents will be out of the loop.... when their child needs them the most.
Just ask her, if she can forgive you.. and if you can both start off anew. Make it all about "her" and not about how hurt you are, but do tell her that it hurts "you" because you love her so much, and you are sorry for your mistake etc. For kids, and remembering when I was a kid myself, having my Parents apologize to me, was VERY important, when they had 'wronged' me or taken me the wrong way. And if they did not, I felt very sad. My own daughter, it makes a BIG difference when I can own up to my mistakes and "apologize" to her... it makes her feel "validated" and then we get back on course.
Good luck,
Susan