If you make this request, the school will HAVE to say that they cannot accept any personal requests for or against individual teachers. This will be because it would be impractical to allow everyone to do this, because most might prefer one person rather than another. It would be wrong of them to accommodate your desire and not that of others - can you see that? And it would be wrong for those with prior knowledge of the school to get to have an influence based on prior knowledge which other parents lack - can you see that? YOU cannot be given preferential treatment.
Schools are big places and your son will be one of many. Classes will be formed to get a mix of ages, perhaps abilities and backgrounds. He is one of many and you are one of many parents too. You are going to have to realise that personal preferences really cannot be considered about these kind of things. Any Head who has worked in a school for a while will know that pandering to your kind of request is opening a can of worms and LOADS of trouble for the school in future from the parent body - it is simply not possible to satisfy everyone's personal preferences which is why it is not possible to accommodate even one, if it is just preference, which yours seems to be.
Why come on here is you aren't willing to hear what people think? Doesn't the fact that huge numbers say your idea is daft and cannot be accommodated tell you anything?
Your son will be fine with the other teacher. Remember that liking a teacher isn't the key thing for learning. And he may love her style, even if your other child or you didn't. He might love her style......as long as you don't give him any kind of suggestion that he won't, or that she is wrong in her approach. You need to back the teacher up, whatever their style.
So wait and see. You may naturally get your preference anyway...or not. And as others have said, only go to the Head when you have a genuine concern about the school, not just a personal preference....you really need to appreciate the school just cannot accommodate your personal preference, because it would be unfair to do so when they cannot offer or accept that from everyone.