I didn't watch the video, but from the comments, I'm going to say it wasn't abuse. I don't believe getting whipped with a belt counts as abuse, if it was meant as a constructive punishment. If it was done randomly or because of anger, then that would be a different story. It's debatable whether or not spanking is an effective form of punishment, but I don't believe there's anything inherently immoral or abusive about it. What you may call "beating the shit out of", another culture may call a standard form of discipline.
I don't agree with posting the video online though. I can't imagine any positive effects that could stem from that decision. But who knows? The mother definitely knows her daughter better than we know her daughter, and maybe posting the video online will effectively improve the child's behavior. I do believe that the fact that the daughter posted those pictures in the first place suggests that the mother's parenting has been ineffective; however, I do not believe that this spanking in particular is bad parenting.
We really cannot assume much from the video alone. Yeah, the girl may seem calm and cooperative now, but again, the mother knows the girls actual feelings better than we do. I would not be surprised if this showcase of cooperation is a guise that the girl puts up every time she's in trouble (I've seen it done with my own eyes). We cannot assume that the mother has not tried to be peaceful with the girl before. The facebook pics may actually be a part of a relatively long history of disobedience from the girl, and this may have been the last straw for the mother. Also, the calmess of the other girls leads me to believe that the rules and punishments were clear in the house meaning the 12-year-old knew exactly what she was getting into.
There is a lot I disagree with in the OP, but for brevity I'll only directly reply to this comment:
"I think up to the age of 16, arguably 18, your parent(s) are 100% responsible for your actions. They chose to bring you in this world and if they can't control your ass then they should get "the whip". "
I'm curious as to what you mean by "responsible." If you mean that parents are the sole cause of a child's actions, then that's false. There are a lot more factors than parenting which can affect a child's behavior: temperament, environment, peer group, culture, etc. Outside of isolating kids from the external world, there's no way a parent can have absolute control over those factors. Also, once a person has reached a certain age (sometime in their early teens), their personality is pretty much formed and there's nothing you can do, within reason, to change them. They've already become their own person by then.
If by "responsible", you mean that parents should be held accountable, then that would be a different, and more disputable, matter. One could argue that children aren't programmable robots whose actions are completely determined by one other agent; rather they are human beings capable of independently forming their own desires and values. As such, it would be wrong to hold anyone accountable for a child's action beyond a certain age. It seems intrinsically wrong to hold someone accountable for something they can't control.
