I would try putting some pressure on the teacher Beety, and see what happens. When I was 12 I passed my grade 5 piano, but my teacher kept refusing to put me in for grade 5 theory for about 18 months and without that I couldn't do my grade 6 piano exam, and so lost momentum and interest in playing.
In the end it emerged that my piano teacher had a student of a similar playing standard, but academically not as bright [brag, brag] and she kept failing her theory exam. It wasn't until my (independent) piano teacher happened to meet my school music teacher, who told her not to be so stupid, that I was entered for (and passed) the theory exam. But by then I had lost the love I had for the piano (and my teacher!) and transferred my efforts to the oboe instead. I wish my parents had been a bit more pro-active and not "let is ride" at the time.
Also, some teachers set great store by the marks of their pupils; and refuse to enter pupils unless they expect them to get at least a merit, preferably a distinction.
Sorry this is so long, but what I mean to say is there may be other issues behind her attitude, and a little bit of parental pressure might help to get over this hurdle.