"The people reading the post are highly likely to be local friends and family who, of course know what school her dd attends."
Fine. But the actual damage stemming from those people knowing which school was involved would be very small.
And they still might not know the teacher involved, so no libel.
"Slander is a serious thing."
First of all it's libel, not slander, because it wasn't spoken.
Libel can be serious when it's clear who the person is, when there's genuine harm to that person's reputation and when the allegation is false. But in most cases, like this one, it's just a thing people say when they don't like what's been said about them.
""Trying to hush parents up" What exactly do you mean? Your very choice of words indicate that it's a dodgy scenario. If you are suggesting that a school is wrong in "every" case you've seen of a difference of opinion then I'd have to say that, in 27 years of teaching, I beg to differ."
I've seen schools try to prevent conversations among parents that they don't like. I've been told by parents of them trying to bring up critical things at Parent Councils and being shut down. I've seen a headteacher act like an infant because they were questioned by a parent at a Parent Council. And then, on Monday, my wife was talking with another parent about acts of idiocy from the school and council in the cloakroom at the school nursery and in the playground, and as she was leaving the school grounds the headteacher came rushing out to try to scold her for it.
Parents have every right to communicate with other parents about what they think about the school, and it's control-freakery from schools to try to shut that down. For a headteacher to threaten a parent with the police because of something they said on facebook, in which they didn't even name the school, is offensive and preposterous.
What the OP put on facebook may have been wrong - neither of us have read it so we can't know. But if you don't see a problem with what the headteacher did about it, if you don't see it as dodgy, then you maybe need to ask yourself if you're not just being a bit tribal.