I think you did everything fine except for your interaction with her. Even if she asks an ignorant question or makes an ignorant judgment, you were not compelled to be rude to her. You chose to be rude, and, in my opinion, there wasn't really a good reason.
You could equally well have said something like this, "The whole course is pretty slow today. I've had to wait on every hole. I feel like as long as I'm not holding you up, it probably isn't a big deal that I hit two tee shots on every hole. If you were having to wait, I would only hit one."
It would accomplish the same thing, and the unpleasantness would be one-sided.
Obviously, you are free to do what you want, say what you want, and to react however you want, but over the years I have found that, generally speaking, things go better if I try to be polite and respectful even to people who don't afford me the same courtesy.