Is it permissible for a husband to allow his wife to visit her family despite his father's refusal due to disputes between the father and the wife's family?

First: Increase supplication to Allah to mend the relationship between your father and your wife's mother.

Second: Strive to reconcile between the two parties, and seek help from those who have influence over them.

Third: Try to convince your father to allow your wife to visit her family, as this is an act of maintaining kinship ties. If he is not convinced, then you are not obliged to obey him in preventing her from visiting without a legitimate religious reason.

Fourth: Search for an independent residence for your wife if she lives with your family, as this is her right and it may help in solving the problem.