All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If what you mentioned in the question is really true that this husband has beaten his wife severely and that he used to harm her, then he is a transgressor and an unjust and a very sinful person. That is because beating the wife has some Sharee’ah conditions which one must not transgress. Indeed, we have issued Fatwa 84120 clarifying these conditions, so please refer to it.
Without doubt, such a mistreatment from a husband to his wife is a clear injustice and an evident transgression. For more benefit on the obligation of having marital relations with one’s wife according to reasonable terms, please refer to Fataawa 88304 and 86618.
As regards this wife going out of her husband’s home out of fear of his abuse and as a way of repelling his harm, then it is permissible for her to do so and she is not considered as a disobedient or rebellious wife by doing so, as she went out while having a sound reason. For more benefit, please refer to Fatwa 91788.
With regard to seeking the permission of the children, then this does not have any effect on the permissibility or prohibition [of her leaving home without her husband’s permission].
Hence, since this woman is harmed by staying with her husband, she has the right to ask for divorce even with compensation that she pays to him and this is what is called Khul’ as we clarified in 89039.
However, it is not permissible for a husband whose wife seeks Khul’ from him due to such harm to take compensation from her.
Allaah Knows best.