Bathsheba - my parents used to stick their noses in all through my education to ensure I got the better teachers at a public school. She did it for all of us, and well - she got a bit of reputation. Which doesn't worry any of us, but I'm not sure it worked out for the best.
For example - she made sure I got the strict mature deputy principal in my grade 5 year (standard 4 in NZ - 9-10years old) and he was really strict, taught really well etc. Theother teacher was OK too - but just much more laid back.
Anyway - Mr B ended up having a stroke halfway through the year and we had 25 relief teachers over the next 4-5 months. And one stayed for 6 weeks - so work that out!! It was a complete waste of a year, and had I been in the other class, things might have been better.
Another example - I was put in Ms S's class in Form 1 (10-11years) and that was cool - cause she was the young funky dynamic teacher. We had that teacher and class for 2 years. Well she won the "tulip queen" beauty pagent, and spent the second year of my intermediate in Holland being a beauty queen!!! Again we had truck loads of relief teachers, including a couple that were old and mean and I hated!!!
In highschool I was in the best maths class with a certain teacher. Mrs C was a complete cow, but great at maths. Anyway, we had a falling out over marks, and I stopped playing netball as she was the senior coach, and have never forgiven her for that (I was really good as a kid at netball.....)

So - yes I think its great to say to the head mistress that you want an eye kept on her, but sometimes if we meddle with our kids schooling, it ends up backfiring on us one way or another. You may find that being with a young dynamic teacher who doesn't neccessarily let kids have their way completely may be just the thing your daughter could use in a school sense (not home of course) - ie humility, taking no for an answer etc. It may be very character building for her.

Thats just my 2c. Another perspective on it. It doesn't matter how much you are paying for school fees - you have the right to help out in your childrens education either way.

Fi