I'm not sure it can be said that it is standard operating procedure for Muslims to beat the women and children. Certainly some do, just like some Christians, Hindus and nontheists do as well.
Perhaps a better explanation would be that people move here so they aren't getting shot at by Muslim extremists yet at the same time do not want their child turning into a Miley Cyrus wannabe.
*Even* if that was what they wanted and not simply socialize like any normal human being. Black eyes and bruises? That is not just a little slap on the hand for trying to stick the finger into the cake.
Honestly, any culture that thinks that beating women and children is ok is the one that has to be avoided. It's about time to quit the silliness that whatever shallow aspects there may exist in American pop culture, the barbarism and inhumaness of many other cultures is far worse.
I'm not generalizing. I'm talking about the specific case above. Someone beat a little girl so hard as to give her a black eye and bruises just to prevent her from socializing with American friends at school. That is hate, ungratefulness and utterly condemnable. It's not a case of "cultural relativism". It's a crime and should be treated as such.
Now, as for the cultural relativism. Cultural relativists will always say "Ha, hypocrite, you condemn this in culture X, but it also happens in yours". Which is just a fallacy. Everything happens everywhere, from the greatest virtues to the lowest vices, because we are all humans, we all have the law of God in our hearts and the potential to be worse than demons in our life. What characterizes a culture is what it considers normative and what it considers wrong.
I can read texts of the Fathers teaching husbands not to beat their wives. I can find priests and pastors teaching the same. Likewise, I can easily find muslim texts and teachers on youtube saying it is ok to beat wives. In both cultures there are men who do it and men who don't. The difference is that Christianity considers it normative not to do it and Islam clearly considers normative to do it. Christians who beat their wives, even if they belong to cultures where it is more common, are less Christian for that. Muslims who do it, even in cultures where this is forbidden, are not worse Muslims for that.