Customer definitely wrong. Restaurant - morally right but badly handled.
If she’s a persistent offender I would have gone with giving her pointedly appalling service. If she complains, be apologetic and say that of course you would understand if in future she chose to take her business elsewhere.
There’s this one woman at our office who actually insisted that the amount of the two take out meals we ordered for some co-workers who couldn’t make it to the lunch with us, be deducted from the bill before we calculated the tip.
Seriously? The lengths some people will go to in order to save a few bucks astounds me. She’d rather walk out of there looking like a total cheapskate than pay an extra 50 cents on the tip. I truly don’t understand people like that, I just don’t.