Would your child have this teacher again next year if they stay at this school? If not, I would cut them out of the loop and deal directly with the principal/head of school as an issue of "appropriate placement." It doesn't sound like your dc and this teacher are ever going to have good chemistry, not matter what is really going on. Since it is a private school, I am assuming you have to commit to a contract for next year very soon. If the admissions/administration folks aren't willing to work with you, then it probably isn't the right school for your child.
We have also gone the private school route and have found it to be more affective to deal with school advocacy issues like business decisions, rather than emotional issues of fairness.
(We have also found that having dh do most of the correspondence and attending all school meetings tends to make advocacy more efficient for us. That is a whole other topic, but it sounds like part of the reason you are frustrated is have your families time wasted...)
