Who knows what the phone conversation was, whatever it was obviously -as you said didn't go well- you expect her to just instantly turn that off and turn to you with a smile?
As you said she's human. Emotions don't work like that.
And here we have what separates the professionals from everyone else.
At my last job, I worked on software used by debt collection agencies. Customer support was one of my responsibilities. Now, most of the guys running debt collection agencies started off as collectors themselves. They know the game. They know how to goad and manipulate. When they called me for support, it wasn't unusual for them to threaten and intimidate--it's in their nature. It's how their business works, and it's their crutch when dealing with any situation where they aren't getting what they want. Some of them would get downright shitty with me.
Here's the thing, though. I never lost my cool with them--not once. Professionals don't do that. Sure, you can be pissed, you can want to throw things, you can want to hang up on them or tell them to fuck off, but you
do not, under any circumstances, ever treat a customer that way. These people are paying your salary, and while they may not have the right to treat you like shit, you also don't have the right to be disrespectful in return.
If customer service is part of your job responsibilities, then it is also part of your job to remain calm and rational. You don't
ever take it out on the customer. You can gripe with your coworkers, gripe to your boss, take a break, take the rest of the day off--do whatever you have to. But attacking the customer is easily the
worst way to go about it.
Yeah, people have pissed me off and treated me like shit. I always give them nothing but polite, calm, rational responses.
That is your job when you're doing customer service. If you fly off the handle, insult them, treat them with anything less than the utmost respect and courtesy,
you have failed at your job. It is a mistake and one you should endeavor not to repeat.
It's true, we're only human, but that never excuses treating a customer badly, no matter how irrationally or inappropriately they behave. If they're making a scene, you ask them to leave. If they refuse to leave, you call the police. Don't escalate the situation yourself or vent your frustrations at them.