This can be such a touchy subject and as one who does not have children, I often opt out as I know people think we childless don't 'understand' (which is true) and therefore have nothing to genuinely say about it.
I am always appalled when in stores and public I see the behaviour of children today. It seems, in my area at least, to increase each decade that the children live literally with NO consquences. When I see parents first try to bribe a child with gift or food, therefore reinforcing their current tantrum/bad behaviour and sometimes just letting them scream and rant as if they can't be bothered, I wonder at the state of the next generation.
I don't have a child, but I do remember being one. I know that if I were to make a scene in public my mother would firmly take me, in a way that suddenly made you realize she was the boss (no hitting, just the stance and sudden quiet stare) and then the explanation of why you should not be loud or whatever you were doing wrong. And if you did continue it there were consquences, that meant leaving the place or sitting somewhere and thinking about it and getting privileges taken away. Having a figure that is the 'boss' that doles out love and also consequences to actions is important, I think, to create an adult in the future that has a real perspective on how the world actually works.
I often wonder had I had children, would people have thought me abusive for the way I would have taught my children? Because I would most likely follow the consquences rule and today parents seem to think that just quiet talking and giving in is the answer, but the screaming demanding physically abusive children I see proves that it is indeed not.
But, if anyone with a child asked me their opinion, I would probably also remain silent, as I know we childless people are often not really considered a source of knowledge on the subject.
I hope your friend can find a solution for her daughter and herself.