I have been fired

[Moomin]

Your mistake was confronting a customer/whatever she was. It doesn't matter that she is wrong, this is not a personal situation but a professional one. Whatever you say will reflect on the company or person that you work for.

The only thing to do in that situation is to leave it to someone that has the authority to have these people removed from the event. Bothering with them as a person without that authority is a sure-fire way to get fired.

Yeah I get that. Been told that already. Thanks. Unfortunately, the person with authority was not able to cope with it, and the boss did nothing, but I guess I deserved the verbal abuse. So thanks.

 

[Moomin]

Actually, that’s made me feel much worse. I was doing a lot better. Now I have to calm down again.

 

[Autistamatic]

Yeah I get that. Been told that already. Thanks. Unfortunately, the person with authority was not able to cope with it, and the boss did nothing, but I guess I deserved the verbal abuse. So thanks.

Actually, that’s made me feel much worse. I was doing a lot better. Now I have to calm down again.

You shouldn't be feeling worse. You did not "confront" the parents - they attacked you verbally and you shouted back once! The father in particular was WAY out of order. Don't go blaming yourself for the incident. You had a badly behaved child, you acted responsibly and the parents overreacted way beyond any reasonable proportion.
I know you feel bad about having shouted back, I would too, but that is not why it escalated - undisciplined and over protective parenting combined with a boss too afraid of whatever threats they threw at them is the problem you had to deal with.
A "professional" decision which does not take account of the personal impact, doesn't get investigated properly and puts the company at risk of being sued by the wronged employee is as "unprofessional" as it gets.
You're well out of it if that's the standard of management you had to deal with. Onto fresh fields and pastures new