I had a similar unprofessionally behaving teacher myself recently and the relationship ended in a very ugly way. This can be avoided in this case I think with a little tact. Though it's possible that the teacher won't respond to tact.
Of course parents should make the ultimate decisions for their children. The teacher is trying to supplant the parents' interest in the child and that's a definite warning sign that something is wrong.
It also sounds like the teacher is putting too much pressure on the child. Music camps, youth orchestra, etc. are fun and the children learn a lot from them. There is nothing wrong with having fun while learning. Not having fun while learning is a recipe for burnout especially at such a young age.
It sounds like your teacher is worried about other teachers taking her student. Some teachers want to keep their best students to build their credentials. How well do her most advanced students play?
You may want to interview other teachers or the pre-conservatory faculty quietly. Unfortunately, this doesn't seem to be a situation where you can seek guidance from your teacher.
I stress, however, that her wellbeing has to be #1.
Please just tread very carefully. It might be a good idea to get some professional advice on how to proceed.
I hear you on the progress that your child is making and how worried you are about jeopardizing this. But a couple of thoughts worthy of consideration:
1) this might be more to do with their talent and motivation and the support you're giving than with the teaching. In other words, perhaps they'd thrive as much or EVEN MORE in a healthier teaching environment.
2) it won't get easier to switch teachers down the road–only harder. It sounds as though you live in an area with abundant options for musical development. Avail yourself of them!
The hard thing is that there is not going to be a good way to gracefully exit without some hurt feelings and possible upset to your daughter. Your daughter maybe highly resistant to the change and it may be difficult to explain your concerns to her in way that she understands, and that doesn't come across as simply badmouthing the teacher to her. I would try to take the high road as much as possible. Thank the old teacher for all her help (even if she doesn't seem interested in hearing in) and focus your daughter on the excitement and opportunities that a new teacher will bring.
You start teacher-shopping before informing the current teacher. Do you carry on with lessons as usual? Is your daughter likely to innocently make any comments about prospective-teacher-meeting experiences? Show doing something in a different way that she was unlikely to have stumbled upon independently? Are you going to *ask her not to say anything* to current teacher? IMO, it's highly unfair to put that kind of burden on a child - and especially when the teacher has a track record of...unusual reactions, assuming fair and objective* reporting of the story.
(Once I correctly suspected that a particular family had started with a new teacher already. However, they had honored my multi-year relationship with them and my schedule by finishing out the term and scheduled ensemble events, giving appropriate notice, and having time for closure. I honored them by treating them as professionally as I would any student, but I did adjust by backing off on things that would require significant follow-up (because I would no longer be following up). Not everyone does this - I've had my share of parents saying at the end of the lesson, this is (was) our last lesson, or worse, texting after the next term had begun and their spot had been planned for, or even no-showing to a previously consistent schedule. I think people must be trying to avoid perceived awkwardness after essentially telling someone you're breaking up. I get it but my view is that there is always a time in a student's educational journey when it's beneficial or necessary to move on, which I communicate to parents early on and some definitely forget when it's actually time.)
*The details are irrelevant but for example, there are certain things I do as a teacher that I could write about and portray in the appropriate, intended context. I could also write them in a biased manner, recounting them as gossipy, chaotic, and controlling. Personally, I would want to know if a parent disagreed or had concerns about what we were doing or not doing and work with me on resolving perception vs. reality. There seem to be plenty of red flags, but OP's last line says it all, perceiving that "best interest of the child" is not being observed by the teacher, that there is a loss of trust in the teacher's guidance. Having one foot out the door can make one view things more negatively.
After saying all of this, the relationship with the teacher is based on trust. It sounds like you may have doubts and do not really trust him or her. To some extent there is good reason not to, gossiping, being unreliable, and distancing you are all huge red flags. However, as I mentioned above, these things in and of themselves can be explained away a bit. My advice would be to really think over your trust in the teacher. After you have thought it over, if you have any doubts, it is probably prudent to change teachers.
Violinist.com is made possible by...
Dimitri Musafia, Master Maker of Violin and Viola Cases
Violinist.com Business Directory
Violinist.com Guide to Online Learning
ARIA International Summer Academy
Johnson String Instrument and Carriage House Violins
Discover the best of Violinist.com in these collections of editor Laurie Niles' exclusive interviews.
Violinist.com Interviews Volume 1, with introduction by Hilary Hahn
Violinist.com Interviews Volume 2, with introduction by Rachel Barton Pine