I have NC as I don't want this linking to my normal name, and the person I mention was (is still?) on MN - I don't care if she sees this and recognises herself, just don't want her knowing my normal username.
Sorry for this long message, but need to share my grief about this, from the perspective of an adult out having a meal with 'one of those nightmare parents'.
It didn't matter what I said to her or how I tried to interact with her son in a calm loving way she still went between ignoring and encouraging his unacceptable behaviour. It is hugely frustrating and embarrassing.
I took the child out of the pub/cafe/venue so many times (not finishing my drink/meal) as she genuinely did not see the issue and stayed there enjoying her meal/coffee/whatever whilst I sat in the car waiting (because I couldn't see other people having their time out being ruined by such a selfish parent).
It makes me feel so sad for the child who doesn't deserve such a parent!
My sons ex GF had no concept of discipline or how bad behaviour affects other people, totally oblivious to it. My son was so kind and patient with her and her young son and tried so hard; he encouraged her to see this was not normal parenting behaviour but nothing ever changed.
It was hard work going out in public with her, she let him run round, shout, scream, fight with other kids... I actually felt very sorry for the little 4 year old. When she went to the local coffee mornings he would slam his hands in the piano constantly, run round, scream, taunt other children and if any 'little old dear' complained she videoed their reactions and put it on Facebook. Awful. Humiliating.
It was the same when she brought him to my house (fuck, I have always been known for my almost unlimited patience, but this got me down!).
One day, in my home, he was so bad I snapped and told him to bloody well shut up, after hours of trying to keep the peace.... She ignored me, apart from a death stare, and once she left my house sent me a text saying "I didn't want to have to embarrass you off in front of (son's name) but we don't use the words shut up". 
I was relieved when the relationship ended! I felt bad for my son, he did everything he could to help her, but nothing was ever good enough.