Without jumping into the debate, because I think there is more than enough representation for each side...
I went to a grammar school. Passed my 11+ and, thankfully, got full funding. There was no way we could have afforded to pay any part of the cost.
I thrived there. It was, undoubtedly, the best place for me.
In year 10, I was moved back to a standard state school, because none of my sisters made it into the grammar school and my mum disliked how holidays and parent/teacher days didn't match up, for example. I got a funded bus to and from school, so it didn't really affect her. The school held a lot of meetings with her to try and persuade her to let me stay.
State school was completely different. No big problems, but very different, and while I still got good marks, I felt unsupported. I walked away with my expected GCSE results, which are good, and the school did try and help me fit in. But I have never been able to forgive my mum for my childhood, and I will never understand why she moved me.
If you need to move her, this is irrelevant. You have to do what is best for you as a family, at each stage. But make sure your reasons are good, and make sure that you can explain them to her and she will understand.