It's the condescension and retaliatory rudeness that I object to, not that the shop is closed on the day the customer demanded delivery.
I don't see any condescension on the OP's part and really no retaliatory rudeness at all. The customer was very condescending, stating pretty clearly that he wouldn't understand about Mother's Day. The OP pointed out that he did understand MD, very well. The customer wasn't taking his repeated, patient responses and needed a very clear demonstration.
What would you have had him do? Keep repeating "We're closed on Sunday, would you like Saturday or Monday delivery?" How do you deal with someone who deliberately and insultingly refuses to hear "that won't be possible"?
To answer the bolded above, I would have had him beckon his mother, the owner of the store, or for that matter, any other employee, to come and tell the woman the same thing. Way back when I worked in retail, that's how we handled difficult customers. This lady is not the first person to walk into a store and demand something that is not possible and refuse to take "No" for an answer. It happens all the time.
IME, it works about 90% of the time to simply have another employee confirm what you've already told the customer. The other 10% they'll keep arguing till they've seen a manager.
I agree that the OP just acted in the heat of the moment, and I can see why. The customer made it personal by saying that he couldn't understand Mother's Day because he was male. And in this situation, when it gets personal, it's awfully hard to keep your cool.
So, while I think what Dr. Manners did was not the best way to handle it, I can completely sympathize on why he did what he did. But again, the best course of action, assuming cooler heads had prevailed, would have been to have the owner talk to the customer.