I didn't like it. I didn't like it at all. But I kept at it because I didn't want to disappoint my parents. It was their thing. I didn't put my foot down and say this is not what I want to do until I was about her age, then I caught hell for it."You're so talented. How can you just give up like that. We didn't raise a quitter...." you get the idea....
...As I got older, I had to face a combination of my self-esteem being shorted because I had parents that didn't allow me the freedom to choose what I wanted to do... I didn't feel like I really became myself as a person until I hit about 27, and I still feel the echoes of self-doubt.... put the horse thing aside and start asking about her other interests.
Maybe she really wants to paint. Maybe she really wants to dance. Maybe she really wants to play soccer. She may feel pressure to do the horse thing because that is what the family does and it just isn't what she really wants to do, then if she's not happy, she's seeking another path in the "horse realm" to go down because she unsatisfied, but that dissatisfaction could be coming from a desire to do something else entirely and figure out for herself what she really enjoys.
This age is the age of breaking off and experimenting with your interests. My best advice is to take an impersonal step back and allow her to stretch her wings outside the horse world a little. See if anything out in the big wide world ignites a passion in her that pushes her past any fear.
In the end, love her and let her know that no matter what, that's never going away.
Apologies to this poster for "cutting up" your post, however the points you made that I included here were my thoughts precisely on the issue...
I'm not a therapist, but it sounds SO CLEAR TO ME reading through these posts that she MAY JUST NOT BE INTERESTED IN HORSES, OVERALL! I know that seems hard for we passionate horse-lovers whom at 13 would've given anything to be in her situation. It simply seems to me like she wants to "find herself", and perhaps for a very shy, emotional girl, (as you've described her), horses may be too overwhelming...
Maybe she doesn't need help making friends, perhaps she's the more solitary type, happier with one or two close girlfriends and the rest of the time to read, write, paint, WHATEVER, ALONE...Just her alone with her thoughts and interests and if she were permitted to do that, w/o any outside pressure to be what others want her to be, she will become less emotional, more happy, more HER!
She may find who SHE IS, and then the family will see the girl they couldnt "see" before, because everyone wanted her to be something else!
No DOUBT YOU LOVE her with all you have and want her to be happy...maybe with no pressure whatsoever (excrpt regarding her completing the basic, obvious necessities of being responsible for schoolwork, being a conscientious and "appropriate" teen, teaching her healthy morals, values, how to treat herself and others, basic child-rearing things (!), she will grow into someone who loves HERSELF AND HER FAMILY...As a parent, that is all I work towards and pray for for my child!
Best to you and your daughter!! :0)