This is going to sound quite pithy, but I think it comes down to feeling that your arrangement to homeschool is your due.
I would bring a stack of business cards and, if anyone interrupts your class, introduce yourself briefly as your DD's outside (class X) instructor and say, "We're in class right now. If you'd like to get in touch with me, please contact me at these coordinates." You are offering educational instruction and should expect the same courtesy as any conventional teacher, including not being interrupted in your "classroom". I wouldn't engage in the "are-you-or-aren't-you-a-teacher" politicking. The school has already decided you are your DD's teacher, so third party heresay is irrelevant.
Do you have a designated space arranged for you by the school? If so, a polite, "Excuse us please, folks, could you kindly take your lunch to another location? Principal X (or whoever) has allocated this space to us for private instruction." should suffice. If you keep your messaging polite and consistent, everyone will ultimately internalize that space as another classroom. If you don't have a designated space, I'd probably want to get the principal's okay for a more predictable arrangement, even if you have to move a bit throughout the morning.
Just a question, but could you help me better understand the legal requirements for you to be on school property?
