That head of year sounds awful! Although it didn't happen to me, I witnessed a similar thing at my school in Scotland. It's really bad. People should have the opportunity to perform and having got onto the A Level it should be their right to take the exam. Hats off to her for all her progress through self-study!!
If it were me I'd definitely stick to my guns about the subjects I was taking! If necessary, I'd register as an external candidate for physics too. I think the best strategy would be to just try to keep them off her back until the exams and don't agree to any more changes in subject. She could say:
- she's not yet getting top grades in the mocks because she requires the time leading up to the external exams to assimilate the content and practice exam technique (this is the point of a course)!!
- she's committed to doing well (give evidence of this, eg. revision time table, having approached teacher for help ect.) perhaps because it's essential to her future plans. Is there a class teacher than can vouch for her?
- also cite previous achievements eg. GCSEs, anything relating to her future career
- as a last resort, say that she understands that the school wants students' performance in exams to reflect well on them and that she, too, is equally as invested in doing well.
I hope that ridiculous teacher leaves her in peace!