أحسن الله إليكم My wife's father is a non-muslim and she was born out of wedlock. She has little connection with him and they are not on bad terms but she fears the sin of cutting ties of kinship due to them not speaking. What should she do to fulfill these rights, or does she need to at all?

The scholars differ on this. The majority hold that he is not her father in the Shariah, since such a child is attributed to the mother, so she owes him no dutifulness and no ties of kinship. Others, among them Shaykh Al Islam and Ibn Uthaymin, held that if he acknowledged her as his daughter and her mother did not have relations with another man, he is her father and his rights apply.