Runs into a student wearing an LBGT pin

Walking down the corridor of the unfamiliar school, I am carrying my crate of things, ready to unpack in my new office. I am feeling good, the offices here are awesome and I will have a whole room just to myself, a small miracle considering the state of staff rooms in many schools. I have no classes today, it is my first day and I need to unpack and prepare for the work which starts tomorrow. While technically there are no classes today, the hallways are not completely empty as this is a boarding school and many students use the building to hang out in the spare time. Despite that most hallways are empty. I round the corner and nearly run into a short blonde girl. She can't be taller than 150cm with relatively small frame and light brown eyes. Her hair is made into two large drills falling on the side of her face.

"I am sorry, I didn't see you." I apologise with a smile.

"Whatever... pay more attention! You nearly toppled me!" she says in the kind of mean girl voice I know from my own years in the school system.

I take a closer look at her I realize that she isn't wearing the standard school uniform. Her's looks to be made from a better material with some small changes that make it less plain. Clearly this should be against regulations. The whole purpose of a uniform is that everyone should look the same so that nobody is excluded due to their clothes. What however catches my mind more is the small rainbow pin on her breast, covering the school logo.

"What is that pin? That uniform? This is clearly against the regulations young lady. Besides...have you no shame?" I go off on her. This might not be me at my best but the girl really rubbed me the wrong way.

She looks at me in clear disbelief. "Do you know who I am am?" she narrows her eyes as she seems to take a better look at me.

"Should I? You are a student here and you will follow the rules just like everyone else," I am not taken aback. "Who does she think she is? I am a teacher and she is a student yet she doesn't look least bit apologetic."

She gets right in my face. "I am Chloe STEWART," she puts emphasis on the surname, expecting me to put two and two together and when she notices I haven't made the connection she continues: "The daughter of the school founder and the board chairman." Each word sharp like a knife. "You should have paid better attention Ms. New Teacher. Now introduce yourself properly and explain to my why I shouldn't call my daddy just this second, tell him how unprofessional and horrible you are and that he should fire you."

This time I am quite taken aback. I let my emotions get the better of me and now I might have crossed someone important around here. Clearly the girl at least thinks she has influence. I weight my options. Should I risk further provoking her and calling the bluff? Or would it be safer to cut my losses and try to make this up to her? If she is correct, this might ruin my career. It would be difficult to explain how I got fired on my first day before even teaching a single class. On the other hand I might back off a step and she could take a mile...