You should ensure that she is referred to a psychologist through the school medical service and you have no obligation to inform the parents that you have done so, if that is the student's wish. The law regards teenage students as "mature minors" who are capable of taking decisions about their own medical needs, whether or not they enjoy the confidence or consent of their parents. While a school will always endeavour to persuade a student of the advisability of working with the parents, where, as in this case, there is an impasse, the wishes of the student should be respected.
When a party returned from an educational visit after school hours, several pupils ere left unsupervised at the school to wait for parents to pick them up. Given that the return time had been notified to parents, should they have been left, and who was responsible for their safety?
Whether it was safe to leave these pupils depends very much on the circumstances. How old were they? Where were they left?Were there other adults within call, who were aware of their presence?
Unless very convincing answers can be given to these questions, this represents a serious failure by the school party leaders to fulfil their duty of care for these pupils.
Had anything untoward happened to them, those in charge might have exposed themselves to a charge of negligence. Unless they can show that they acted reasonably in the circumstances, the headteacher should consider taking disciplinary action against the staff involved.