Avira, my problem is your equating of decent behavior with getting a hat.
I understand that the kids in MO schools have these problems, I have no direct experience with MO schools, but I heard and seen some … Again, I am sure some of your influence is positive. I also appreciate that you seem to know something about parents you are dealing with. Teachers I had issues with, did not bother to learn anything about the family.
That said, why does your influence leads to their desire to get a hat, out of all things people can do to improve their middos? Can you think about influencing them in such a way that the parent calls you to say – thank you very much, my son today said a wonderful dvar Torah, asked me to tell him about my grandfather and how he kept Yiddishkeit in Hungary, and cleaned dishes after the seudah?