I work in a private school. All bar one of the teachers is qualified (and she is a native speaker of the language she teaches and has been teaching 30 years, and much better than any state school teacher teaching a language they don’t actually speak them self, as happens regularly in state primaries with MFL). All bar 2 have also worked in state schools as well as this private school, and trained on the same courses as state teachers would have done.
meanwhile, while state schools technically have to employ teachers who are qualified (if under LA control), there literally aren’t enough teachers so more and more TAs are put in front of classes, at least part time.
There are some amazing teachers at my private school. There are also some who are just ok. The same was also true of state schools I’ve worked in. Behaviour at my current school is basically not even a consideration, everyone just behaves. This means children can do well even with average teachers as they can concentrate. At the last state school I worked in, behaviour was so poor that children struggled to make progress even with outstanding teachers, as the teacher spent more time outside the classroom dealing with issues than they did supporting those who wanted to learn.
Just to add some balance to the ‘private school teachers aren’t even qualified, state teachers are’ and ‘state teaching is better’ arguments! 🙂
That said, my daughter is about to start in a state school as we just can’t justify the fees for prep even with a discount. Unfortunately all those fee increases are unlikely to be going ti staff!! OP, it really feels like you can’t afford it anymore - so contact the school and say you may have to leave at Christmas - my school would find a bursary for you short term. And seriously look at moving your daughter now.