hmm it doesn't sound all that great to me (but maybe I am equating your experiences with our own). When I spoke to the current teacher about whether she thought I should change, she said she had noticed that my dd's hold was not optimal. She asked me how the lessons went and advised first discussing it with the teacher we had and trying to change. Essentially what you are doing.
When I brought something specific up, T1 would comment on it during a lesson more, however she did not do what I would have liked her to do which is actually work on it in a child-orientated manner during the lesson. I did ask her specifically to do this but she did not I think have a training whihc included how to do this in a playful manner IYSWIM? I had a trial lesson with T2 which was what I imagined a lesson should be like - and she advised me to change afterwards. I feel quite lucy she was able to squeeze dd in, she is very much in demand but wish as I said below, she had a bit more time and it was not all so crowded, one student piling i n on the next etc. In fact I'd rather pay extra for a longer lesson to avoid that but she just doesn't have time to fit more in.
For this reason, (hit me hard if I'm mad ) I am also trying to set up an additional lesson for dd every fortnight with a very qualified (elderly) teacher who has trained some very successful musicians. This sounds very pushy. Actually she was recommended to me by a music teacher dd used to have at school who was just lovely to dc so I think this woman has time, experience and she will have the kind of approach I prefer. At the time she was recommended to me though our timetables didn't match up which is why we started with the Russian teacher.
This T3 (!) is away at the moment but I am hoping we could have a more tranquil lesson with her every second week in which dd could be guided along to progress with new things if the teacher is willing to consider that
I find T2 really does know how to teach to dc. She reacts when they look tired or frustrated and changes the pace/a ctivity (our previous teacher did not for instance). You can be a great musician I can imagine without having the knack for dealing with dc.
I am very happy with the change though and I found despite the quite rapid progress dd made with T1, her hold and stature left something to be desired. T2 has very gently but successfully altered that in just two lessons. As to bow hold, Dd gripped too tightly and she has learnt to loosen her hold now. I liked the way this taacher worked on that for instance. This as opposed to T1 who would comment on it to me and I would tryand figure out some way of dealing with it during the week IYSWIM. Oh the joy...
You are lucky you have some options : continue wtih current teacher, change to the one you had a trial lesson with. (Could you not have a month or two double lessons maybe). I know it gets expensive but really you need a lesson your dd can learn from. You also perhaps have the option to go back to the previous teacher. They are probably all good teachers but do they get through to your dc? I think that is key really, otherwise I can see a dc getting frustrated and giving up.
Wonder if your teacher would be prepared to work with a theory book alongside the actual violin lesson, so you and dd have a better grasp of what is going on theory-wise?