It appears that the OP has tried to communicate to the teacher with no positive results. The teacher appears to be unapproachable and inflexible.Without opening means of communication with the teacher, this is a very one-sided perspective. Before getting riled up about notes in a planner and “going over her head,” as suggested, have a conversation.
Perception is reality; if a parent believes their child is struggling at school they should do what they believe is necessary to help their child. Even if it is straightening things out between all. The school systems are there to help and would not want a parent and child to struggle because of issues they are having with a teacher. No one should tell them they can't ask for help even if it means going over their head.
I know I would and pity the child that has parents that are unwilling to look for a better school experience for their child.
There is nothing wrong with challenging the school system, they are never perfect and are obligated to help all kids.