Are you jealous? If you don't need time with the teacher, why is it a problem that she feels she does?
Why do you feel that her speaking to the teacher at drop off/ pick-up is going to inhibit your relationship with other parents?
I have literally no idea why this woman's behaviour is any of your concern at all. If you need to speak to the teacher, call the school and make an appointment.
You sound bonkers. There are always parents like this. I don't understand, at all, why is it impacting on your own eqanimity? Surely you and the other less needy parents just roll your eyes and bond that way?
You are in danger of making the school think you are the needy one, for causing a fuss about pretty much nothing (well, I don't like the way she discusses a lost hair and with the teachers, and she's loud')
I am boggled. What would you actually say to the school without making yourself look like an arse, and that wouldn't be met with a polite 'I'm afraid that's not one of the criteria we consider when allocating classrooms, mrs x'?