Neither of them are likeable people, IMHO. Not condoning her actions, but I feel like someone had to play the big boy here, and nobody did.
“Crazy” was wasting an hour or more taking this no doubt irate woman down to the sheriff’s station, booking her, driving her to the county jail. All for something that could have been resolved by “my badge number is ###, my name is Officer —-. Are you finished yet, ma’am?” He broke your rule: he engaged the crazy instead of letting her rant till she’s tired of it and laughing about it over a beer later that day.
Better yet, replace the traffic cop with a camera issuing a ticket for 69 in a 50. She can rant to the mailman for all it’s worth. Use the police freed up for other things, like investigating non-traffic crimes. A friend had her home vandalized last year. Police couldn’t even be arsed to show up and take a report.