I would talk to her and get her to see that the awful way that these girl behave at this particular stable is not the way "we do things in our family". I'm sure you already have...
Explain that you understand that she needs to fit in but that she needs to leave the stable attitude at the stable.
Explain that you work hard and make huge sacrifices for her to persue this interest and that if she continues to behave like an arse at home then you will simply pull the whole things and spend the money on something nice for you instead
Does she do many other things or is this stable a massive part of her life and week? Perhaps you could encourage her to have (nicer, good influence) girl-friends round for a DVD and sleepover to remind her that these are her people - not that grotty bunch at the stables.
When my younger daughter (now 15) started to go into a particularly stroppy/ slammy/ flare up and give you a mouthful phase, I actually re-introduced the star-chart. We all know that there are huge parallels between the toddler and the teenager years, right? If she went a day behaving really well, she got a pink smile on her chart and if she did something unacceptable, she got a black sad face. The amount of pocket money she got on a Saturday morning was determined by the number of pink smiles she'd got that week. Maybe you could figure out some sort of inventive scheme whereby her behaviour is demonstrably linked to rewards?
Ultimately though, and in the long-term, perhaps she could have all her Christmas and birthday money from everyone put towards a pony of her own and be part of the nicer stable? I'm sure it's a enormous financial commitment though - I'm really glad that my DDs are not into horses.
Good luck