This is slightly off the subject, I know, but once I taught my own children for a while when they were in high school. The problem was how they should address me in front of the other youngsters. My daughter just called me 'dad' and that was that, and my son never really called me anything. He certainly didn't want to call me 'sir', which was good as I hated being called that!
Well, your friend may be party to the information if she teaches your child but I agree she is bound by professional conduct. My close friend taught in my kids' school for a while and she was more worried about what the kids said about her!
Anyone working with children/young people/families etc should have it made clear to them at interview or soon after that anything they discover in the course of their job is to remain confidential. As said before, there is probably not much to worry about, but make it clear to the Head what the situation is and go straight away to see her again if you suspect something untoward is going on.
Would you feel the same way if someone you knew got a job at your GPs surgery?
Is there a particular reason why you are uncomfotable with this person working at the school or would you be just as uncomfortable with anyone you knew going to work there?
Moving schools is a big deal for most kids, think rationally here and ask yourself what would happen if this person got to know about things you have discussed with the head? Obviously, you can ask the head not to discuss with this person.
While I am pleased for her as she's worked hard for this career change, I am also a bit awkward about it.
I've spoken to the headmistress recently about personal issues within our family which I really wouldn't want my friend to know about. She's a friend - but not close friend - and also lives five doors away from me which just compounds the problem I think.