Pssst, Floydie .....normal sibling behaviour especially at 15 and 11
What's not normal, of course, is the situation you are in. Glad D11 went to the counselor.
My suggestion is that you tell D15 that you worry because you love her and that you want her to go and see someone, just once. If she never goes back, fine. But explain that sometimes talking to someone who doesn't know you and is not allowed to repeat anything helps. Sometimes it doesn't and that is cool as well.
I made my D go at 13 (last year). She declined to go back and said she would rather talk to her friends. That she felt weird talking to someone she didn't know.
Also the fact is your D opens up to you. So, you could always go to a counselor for help for your D and her concerns. Then try thee practices etc with your D. Just a thought.
My IC gave me some good advice when I expressed concern.