Is it permissible to divorce one's wife based on her family's request, especially after having a child with her, given that the wife constantly insults and abuses the husband, neglects her marital duties, and there is no hope of her reforming, and would that be considered an injustice to her?

If the wife stipulates in the marriage contract that she will remain in her country, then her condition must be met. However, if she does not stipulate this, she must obey her husband and move with him. Otherwise, she is considered disobedient (nashiz) and forfeits her right to maintenance. Divorcing the wife in this situation is permissible and not unjust, especially if there is a need for it due to the wife's bad character or the harm she causes the husband. Nevertheless, it is preferable to keep her as a wife for the sake of the child.