Through no fault of her own, bless her she's not getting to do what she wants as a career
I know things have changed tack and are looking more positive since you posted this but just wanted to say that (only imo of course) subject choices and schools up to age 16 have absolutely no bearing on a child's chances in making it in the performing arts - as long as they're getting their training and support from somewhere of course.
My daughter is currently in Year 10 at Tring Arts, on the dance track. She started in Year 9 but that's only because she really wanted to, we're within travelling distance and that's the school that offered her a scholarship (I'm not rich!) We also applied for non specialist schools and I'm sure she would be doing just as well, and having similar opportunities, in some of those.
Other children will join the school at 16 and will have just as much chance of making the arts into a viable career (ie not much of a chance 
) as the children that started there in Year 6 or Year 9.
Even ages 18 or 21 aren't too late. In fact, I have one professional musician/actress/singer friend who did academic A Levels, went to an academic university, trained as a teacher, headed up a faculty in a secondary school and then went to Mountview to train in MT. She's in her 30s and making a pretty successful career.
If you have the talent then a particular school accepting you at 14, or even 16, is not an essential requirement at all.
Good luck to you all in getting the places you are applying for though.