It's human nature to sink to one's lowest level of fear. By default, that's what our minds are wired for and do. In the case of this lady, she imagined a sexual pervert using a drone (-which in itself is a mystery, and therefore something to be feared). By the time that she got to you, all of that negativeness gushed out into an almost rage. What could you have done?
I would, first, have asked if she would mind if you brought your drone back safely before talking with her so that you could give her your full attention. Then (-after landing) I would have just listened to her (-Let her vent her feelings). Then tell her that you understood how she felt, and that you were photographing your son/daughter from a different angle, and that you were proud of their accomplishments! Then you could mention the legality of the flight, with a follow-up of "Do you still think that what I'm doing is wrong?" The idea here is to develop a two-way conversation. If she returned to cursing, I would ask her to please express herself without profanity, as it was against your beliefs. If no progress then, I would apologetically say that you would respectfully have to disagree, but thank her for her slant on the activity. -Perhaps even with a conciliatory rejoinder that you would get a written approval from the facility before the next practice.