Is the wife entitled to seek divorce or khul’ due to the husband's severe beating and abuse of their children, or is that permissible only if the harm is inflicted upon her?

The fundamental principle is that it is forbidden to seek divorce unless there is a valid excuse, based on the Prophet's (PBUH) saying: "Any woman who asks her husband for divorce without any [valid] cause, the scent of Paradise will be forbidden to her." Among the valid causes are the husband hitting or insulting his wife. However, the husband hitting his children does not permit the wife to seek divorce unless it causes her apparent harm and hardship.

The woman should consider whether divorce will protect her children. The father should be advised and reminded of mercy and compassion and warned against injustice, based on the narration by Aisha from the Prophet (PBUH): "What they betrayed you with, disobeyed you in, and lied to you about, and your punishment of them will be calculated. If your punishment of them was commensurate with their sins, it will be even, neither for you nor against you. If your punishment of them was less than their sins, it will be a virtue for you. And if your punishment of them was more than their sins, then the virtue will be taken from you on their behalf." And also based on the Almighty's saying: ﴿And We will set up the scales of justice for the Day of Resurrection, so no soul will be wronged in the least. And if there is [even] the weight of a mustard seed, We will bring it forth. And sufficient are We as reckoners.﴾