I was going to suggest that you be sure to bill her the time you spent posting here and reading the responses . . . because her email was pretty condescending and rude. Probably she didn't mean for it to be, but it was.
Pretty much my entire family is self employed. Anyone who is self employed knows that a small percentage of potential clients are just not worth the hassle whether you need the money or not. Emails can be tricky, though, as your lose the nonverbal clues to whether someone is being snarky or just clueless. Most of my family just advises to state your estimates or fees, then stick to those no matter what BS response you get. Sometimes people come around and are awesome in the end, and other times not so much, but you never want to give someone a discounted rate when they show any signs of being a PITA.
Sounds like you handled it fine. Good luck with everything!