Hi! I'm wondering if you eventually know about any korean dramas that deals with child abuse? It doesn't have to be just physical, but also mental abuse and neglect, etc.

definitely watch kill me heal me..
Not Kdramas but kmovie- Hope. 
I Hear Your Voice - neglect
*spoiler*

Sassy Go Go has a character that is abused by the father ... well he isn't a child but still he is young
Hotel King
Tree of Heaven
Love Letter
Introverted Boss
Good Doctor
Glory Jane
It's Okay, That's Love


J-Dramas
Hokuto
Daisho
Shikaku Tantei Higurashi Tabito
Angry Mom
Bachelor's Vegetable Store
White Christmas
Empress Ki
+1 Healer
High School King of Savvy (depending on how you look at it)  reverse the roles or don't, the position the lead is put in is child abuse any way you look at it
Hwang Jin Yi
I Remember You
Missing You
Moon Lovers
On the Way to the Airport
Rebel: thief who stole the people
+1 Sassy Go Go
The K2
The Royal Gambler
The Village: Achiara's Secret
+1 Voice


So though most of these don't include child abuse as the main theme, I'd suggest that all of these either have past child abuse as a theme for the protagonist's actions, contain child abuse as a plot point, contain elements that are historically normal but would result in jail time these days, or treat as normal, something I'd consider child abuse. (also lets not forget all the scenes of mothers and fathers hitting their children over the head that we see in asian dramas). 

Angry Mom deals entirely with bullying of children by both adults and other children.