The teacher is not behaving out of turn. They are doing their job and are taking a course of action which isn't beyond what anyone on this thread thinks is unacceptable.
The parent is abdicting the responsibility of explaining how the teacher is the authority and is speaking in that way for a reason and it is not appropriate for the daughter to copy this.
The OP seems to think that she should complain and get the school to deal with the matter. The reality is this is a basic parenting situation which has happened at home, not at school and it is for the parents not the school to deal with.
The OP has made a big song and dance about how she is a great parent yet, wants to blame the school for this rather than do parenting herself and to teacher her own child appropriate behaviour for a situation.
Thats one of the things thats really boiling my piss, and I see happening over and over again - parents who don't want to parent and think its all the schools job and then seek to blame the school when their child doesn't behave correctly.
Parents are capable of teaching their own children manners. This is in the realm of basic manners. It is not the child's job to tell her brother off. It doesn't matter in what manner she is doing this, its just not appropriate and THAT is what the OP needs to tackle not just the manner in which she was by what she says is copying what the teacher does.
The reality here is that kids copy how others behavior whether that be other kids misbehaving or how adults behave. They have to learn what is acceptable and appropriate and what is not. They need their parents to guide them in this. And they need to take responsibility for their actions. If all they see is their parents failing to take this responsibility they will also fail to take responsibility and learn that they can just constantly blame the school or teachers and then they will behave like brats which is only going to lead to a whole pile of other problems.
The OP wants to complain rather than parent. Thats the bottom line. And thats a really common thing thats breaking teachers.
I would love the OP to explain why can't take this on, and why it is down to the school and not her to deal with. The OP really can't claim to be the great parent she thinks if she does this every time her kid acts up - because thats what will start to happen. Then she will go into school in combat mode and gradually will totally alienate the school by being THAT parent.