Is it permissible for a man to sever ties with his kinsfolk (his nephews) who harm and insult him, and whose visits he sees as bringing nothing but further harm and humiliation, even after his sons have tried to convince him to maintain family ties?

The womb (kinship ties) holds a great status in Islam. Allah connects with those who uphold it and severs ties with those who sever it. Your father must maintain ties with his brother's sons and daughters, for they are relatives with whom connection is obligatory. He cannot be considered one who upholds kinship ties unless he connects with them even when they have severed ties. He should be patient with any harm he receives from them, seeking reward from Allah, unless visiting them would cause him harm, in which case the obligation of visiting is lifted from him. He must also give his brother's sons and daughters their father's share of the inheritance if they have a share with him, and he must not wrong them in anything.