I live in New York City when my son was in middle school I wrote the teacher through his communication book to request to come in and observe.

Yes, I have emailed the teacher or called to let her I was going to stop by and observe. It was usually during recess especially when he was in preschool. I didn’t want to confuse him because if he knew I was around he would want to go home. 😂

Research the laws in your state.
Most schools have cameras that monitor the class and property and some allow parents to use their surveillance system(s) to view their child's behavior while in class or on the property.
The Administration has no say over what the law(s) are, and if the Law(s) say that you are allowed, then I'd just advise the School/Principal/District of your actions, and if they say no, guide them to the Law(s).
Show them that you are not afraid of doing your research and then hold them to the Law(s).
Don't be Belligerent, just ask a lot of questions, and when they say or do something against one of the Law(s), then inform them about it.

They full of crap.... Lol

I just told her teacher i want to drop in and observe ashley at school. Her teacher said i can come visit ashley anytime. Ive visited several times.