What is the ruling of the Sharia regarding a wife's refusal to allow her children to visit the husband's family after a severe dispute, and her threat to seek a divorce if they go, and what is the ideal course of action for the husband in this situation?

The husband must be just between his wife and his family, and prevent injustice between them as much as possible. It is forbidden for him to submit to his wife in preventing his children from visiting their grandmother, for that constitutes disobedience to parents and severing ties of kinship. If the wife requests a divorce without a legitimate Sharia reason, the husband is not obligated to divorce her, and he may keep her in kindness or divorce her according to what is in their best interest. The husband must alert his family to the حرمة (sacredness/prohibition) and danger of slander (qadhf), as it is one of the grave, destructive sins.