I (F25) am having some issues with my professor (f30s) and need advice

I am a mature student going back to school for a second degree/career change. I'm in my second term of my program. The course I'm taking is a two part course and I'm in the second part of a course which is taught by a different professor.

In the first part of the course I did amazing got an A+. I'm not doing so well. I feel like I am not doing well not because of a lack of understanding of the material but a lack of understanding of my professors expectations. This program and this class in particular is very rule and regulation based, It's the kind of thing that is generally right or wrong and my professor is deducting marks based off her personal preference of things like bolding words or word choice. This would be ok as it is neither allowed or rejected by the rules BUT she never told us her preference. And I don't think it is fair to deduct marks for that. When I spoke with her (and I add I was very polite and respectful approaching it from the angle of wanting to understand where I went wrong) She said in the real world different bosses will have a preference you have to conform to. I figured that was a valid point and have since tried to conform to what she wants.

But her instructions are so unclear. She contradicts herself. She rarely puts things in writing so you don't even have something to go back and reference to. Any time you ask her a question she freaks out and is rude. She was say you should pay more attention and her instructions were clear. This is not just me, basically all of the other students feel the same. She said in class our exam was closed but except we can use our textbook then the next class she said no textbook and then the next class textbook ok. She didn't post an exam information post in our digital class (It's standard for profs to do that). All students were confused, I emailed and to ask her and she said "If you paid attention to my instructions you would know it is closed book you cant use your textbook".

Today I went to the exam and I arrived 10 minutes early. She had already passed out papers and given all the instructions even though class hadn't begun. I sat in a free seat and asked for a paper and she yelled at me because for some reason no one was supposed to sit in that seat. She never asked us to come early. I think it's unfair to give the instructions before the start of class when all students are not present and get mad when they don't know.

I could give a million examples like this... I'm so fed up with her rudeness. I could put up with that but I feel like her unclear, contradictory instructions and refusal to clarify when asked questions are severely impacting my mark and it's not fair. I do not even want to go to her class sometimes because I feel she confuses me more.

I don't know what to do. Should I speak with her directly? I feel she would get defensive and yell at me. Or I could speak with the program co ordinator (same as department head I think?)

Tl/dr:

My prof is unclear and contradictory. When asked questions she gets rude and defensive. This is a problem most students seem to have. Should I talk to her or go above her head?