I'm having a similar problem with my DS1, who is a bit older than your DD (he's in yr 5). He generally loves school and participates in class, sometimes, I think, at the expense of the quieter children. All his teachers so far have been women and have all been quite maternal and gentle. He has a male teacher this year who doesn't seem to be letting DS1 speak up and who terrifies him, and I'm concerned that DS1 is going to lose his enthusiasm for school.
As far as I can tell, the teacher is perfectly competent and although i don't like the sound of his teaching style I don't think I can do much about it.
The strategies I'm working on are:
mention to the teacher at parents' night that DS1 is unhappy at school for the first time since he started, and could he please keep an eye on him for me.
mention it to the head teacher as well, really just so that if things get worse the head has some idea of the context.
I've spoken to DS1 about it being appropriate to give the other children a chance to speak up, that his confidence might be intimidating for them. We've spoken about humility (it's an RC school). I've tried to get him to imagine what he'd do if he was a teacher with a DS1 in the class (that didn't really work). I'm trying to make home time a bit more special for him.
I don't know if any of these things would help with your DD1. My problem, and I'm sure this is even more so with a yr 2 child, that the sort of techniques that help us to cope with shouting, being ignored, sarcasm etc require a great deal of maturity. It's a lot to ask of a 6 year old, let alone a 9 year old.