I don't know if this would interest you, but have you considered coaching? As in, life coaching? I realise it's an uncommon solution and one that many people don't know much about but I'm currently studying to be a youth coach (I am not offering myself or selling anything - I'm not even qualified yet!). It's a bit more specialised than life coaching because the issues children (up to 18) have, are different to those adults face.
A youth coach may be the ideal solution and there are actually lots of them about, some based in schools, some in the community. Coaching isn't like counselling, it's got a very different focus. I find that young people respond very well to coaching because it's essentially problem solving. To put it simply, a counsellor or therapist may try to understand where something has gone wrong in the past, so that they can rationalise/overcome the 'trigger', fix a 'deficit' in your child's behaviour/coping abilities. A coach wouldn't dwell on the past at all - a coach helps you come to a positive decision about your future, based on where you are, they assume (and as a result, confer onto their client) that you are absolutely capable of making a good decision (with help). BIG confidence booster there?
I think it might work for your DD because it would be a way of working through her anxiety not as an illness, but as a problem to be solved - it may be empowering for her, even at 14, to realise she can make choices about her own life that are about acting, not reacting. They may not be 100% free choices (at 14, you have to fit in with your parents and siblings etc) but there are choices nonetheless. If she's really entrenched right now, a coach could help lift her focus from what she wants right now, to what she wants long term.
I don't want to promote anyone in particular, but I know there are a lot of very good specialist youth coaches out there, and I'm sure if you google you might find someone in your area to try? If you don't want to stop the counselling, they may be willing to work alongside that.