Thank you for your kind comment.
The Housemistress' approach does not seem to be helpful.
Something is going on. Hopefully you can have a rational discussion with your daughter on a "meet her half way" basis. You are concerned, not because you have her future mapped out and have invested accordingly, but because you want her to be fulfilled and have a career that is right for her.
I suspect she is saying that she has had enough of being a prize racehorse groomed to jump the hurdles necessary to canter into Oxbridge and into a high-flying professional career. She sounds like a nice and thoughtful child.
It could well be that she wants out of a boarding school. She will not be the first 16 year old who wants out. If so discuss alternatives. Competitive sixth forms may be full, but within the private school network there is scope for schools to phone each other and find places for a child who wants/needs a fresh start. Especially for academic high flyers. Are you near a town with either good private or state academic sixth forms?
Time out, post GCSE, is not the worst idea but it would be difficult to then go back to take A levels within a school setting.
It could also be that she senses that she wants something other than an academic future and a career working long hours in an office. This is not an unreasonable preference. I have a friend who has built a sound business providing at-home beauty treatments to busy, often well-known, people, eg before red carpet events. Money is good and time flexible, she is her own boss, its suits her sociable personality and provides a channel for her drive and organisation. However she would not have wanted to stay in a salon working for someone else and getting backache. I suspect that long term the same will be true of your daughter.
I am not sure how best to turn down the heat and have a sensible discussion. However you could start by acknowledging that your daughter owns her own future and that you are pleased that she has started looking at options. Then start looking at ensuring that at 16 she is not setting those options in stone but keeping them open.
Might it be an idea for her to see a careers guidance councillor who can take her through options?
A decision to take a vocational course at 16 implies she is committed to that vocation. Work experience.....Even if you need to pay them, get her into your local beauty salon for a couple of weeks over Easter and for most of the summer. If she wants to change the world, she is unlikely to do it sweeping hair clippings off the floor. If she is prepared to graft and can see herself owning that salon or using the skills in a different context, then she needs to work back from there to see what qualifications will be most useful. Depending on the college and the quality of the teaching, a basic BTec may not be.