That's good stuff.
I feel bad for the mother, obviously she isn't doing a good job as a parent; but she's still trying and hasn't given up yet. It must be so heartbreaking for her to try and sit through that, pretending to be indifferent to the screams.
It made me laugh, when the mom showed the slightest bit of resistance to restrain the girl when she was going to charge the brother with the camera. The resistance was not enough to prevent her from charging the boy, so the girl was obviously just looking for that reaction from her mother. (Further escalating her underlying issues) Then her screams turned to Mommy, stop him with the camera. - Now what's the mother to do, She can't show that she's giving in to the girls demands, but she needs to show an authority over her other child to set a strong example. She wants to tell the son to leave, but that's just giving in.
I would be hard to deal with a child like that, they are like a wild animal. Where do you even start. Do you just lock them in their rooms. What if they hurt themselves? Judging by this video, I think this particular girl would be fine, if you just locked her in her room. She showed moments of control. I guess if I was her parent, I would just start locking her in her room, whenever she behaved like this. I would tell her she isn't capable of behaving appropriately in public, unless she changes her behavior. Whatever damage she did to her room, she would be forced to deal with. If she break stuff, tough luck. Next you would need to have a sit down with the older son, and tell him that this is serious and it's a matter of saving his sisters life, He needs to realize that it is his responsibility to set a good example, and when situations with the daughter occur, he needs to listen, and do exactly what you say. If he doesn't follow along, he should receive the same lock down treatment.
I think of an unruly child, similarly to an unruly dog. Establish dominance, set clear boundaries, Enforce those boundaries, Support everything within those boundaries.
What about physical punishment? Would a good spanking be a benefit to this child? Screams can quickly turn to tears. Although it can damage the relationship, pain is such instant negative reinforcement. It works really well for stopping behavior. I think a child gets this way because of too much coddling, so she probably would be fine after the initial shock wears off.