For what it may be worth (probably very little), I have only ever had one experience remotely resembling the above, although this is somewhat unsurprising, since I have hardly ever taught at all.
Years ago, I was approached by the mother of a very musically talented 11-year-old with a request to teach her. My initial instinct was to decline politely and, on the face of it, this is what I should have done at the time, since although I am a composer I was expected to teach this girl the piano! I reluctantly took her on nevertheless and she made some good and rapid progress for a while, whereupon her mother began to question me very insistently about when she would be taking which exam. At this point I felt obliged to remind her mother that her brief had been that I teach her the piano rather than specifically to pass exams and that, unless there was a specific academic requirement for her to have passed a particular exam in order to entitle her to enrol for a particular course, I should be the one to decide when she should take exams. This did not go down well, but it was grudgingly accpted. Not long after this, the student herself asked if she could go in for an exam and I agreed that she prepare certain pieces on its syllabus if she wanted to take it; this then prompted her mother to want to know why she couldn't take it sooner than I had suggested. I replied that her daughter clearly had no idea about giving performances and that, since a piano exam would be just that - a performance to an audience of one, but a performance nevertheless, she was not mentally prepared to take one; I added that the reason for her ignorance here was that she'd never attended any live music performance herself. I took her to a piano recital soon after that. It did the trick; she soon went to plenty of other concerts and then passed her exam with flying colours. She was also a gifted cellist. When it came to decisions as to specialising in particular school subjects at the age of 13, however, she decided against music becase (a) she would always want to continue playing both instruments in any case and (b) she did not want to consider a career in music because there were so many talented players out there that she didn't think she'd make a success of it and that failure would almost certainly mean that she'd have to end up doing what I was doing! I could have burst out laughing (especially as she was the only person for whom I was "doing" it at that time) but managed to control myself. Many years and four university degrees later, she became a well respected metallurgist and the extent to which she still performs may best be illustrated by the fact that, having formed a piano trio (in which she was the cellist) and arranged a début concert for it, the pianist suffered a serious accident a few days before the performance and she found another cellist to take her own place and rapidly learnt and played the piano parts which, considering that the main work was Mendelssohn's D minor trio, was no mean feat - well, not for a professional metallurgist, anyway.
In short (and I apologise for the digression), never take any parental interference of the kind to which attention is drawn in this thread - but do first of all ensure that the line separating such interference from genuine and constructive parental interest is clearly understood by both parties beforehand.
Best,
Alistair
Topic: parents and interruptions