I realize that. But when dealing with rude people you basically have two choices: you can take it personally which it probably isn't, or you can say to yourself, "Self, that person is a rude person. I bet that's the way they treat lots of people. Rude!" and move on.

You handled it well. You told her employer and advocated for better treatment. Go one step further -- don't take her rudeness as a personal judgment; she's just a jerk.