Without more details, it’s hard to comment. I read the situation very differently: I imagine that whoever it is is trying to make your life easier. They probably figure that you would want them to go via public transportation but that your kid is giving you a hard time so they were trying to help you.
I could believe that a Rebbe or member of Hanhala noticed you dropping your kid off one day and was surprised because many/most classmate come on their own. When they asked why you had driven, your son answered “she drives me every day” at which point they encouraged him to come on his own. They probably thought they were teaching derech eretz!