What should I do to maintain kinship ties while there is a rift between my parents and their relatives, especially after my father threatened to sever his relationship with me if I connect with them?

Islamic law has commanded maintaining kinship ties and forbidden severing them, even with those who sever them. It is not permissible to obey one's father in severing these ties, as obedience is only in what is good and permissible. You must maintain your kinship ties without your father's knowledge if you fear his anger. Strive to gently and courteously advise your parents to maintain their kinship ties and explain the ruling of Islamic law to them. You should also endeavor to reconcile your parents with their relatives, for reconciling disputes is better than the rank of fasting, prayer, and charity. It is permissible for you to convey pleasant words, even if they are not entirely true, for the sake of reconciliation.