Good luck trying to get custody of a relative with living parents in a country like that.
Unless the man gives up Cheol willingly, which he would never do, it's an uphill battle and will most likely end in mandated counselling while the uncle gets banned from their lives.
Even parents struggle to get custody from each other in situations like this. Cheol needs to be beaten within an inch of his life for anything to happen, and that means his father could be separated via a restraining order while the mother retains custody. Again, the uncle won't be considered. And since she's a pushover, the father will still be around unless someone reports him. Court cases like this take years. Restraining orders dont really do anything unless you get attacked again and the asshole won't even be locked up most of the time.
The world doesn't work like on TV.

Okay… so why can’t the uncle take him in then??? Was it stated and I didn’t see it when reading??
He looks better off, seems to care about him, dislike his brother overall, and for how he’s treating his nephew, blah blah blah. And I get that a kid (though old enough) is a lot of responsibilities but still. I don’t get it.
I wish he would have taken him away you know. The man is suffering.
And I hope the hell the uncle won’t send the brother instead to study abroad. But I feel he might because then the father would turn around blaming Cheol and beating him.