Is it permissible for me and my wife to perform Hajj despite our estrangement from my sister and brother for more than six months due to their insulting my wife?

Your Hajj and your wife's Hajj are valid. It is not permissible for a Muslim to abandon his brother for more than three [days], and you must mend what is between you and your relatives, for severing ties of kinship is among the major sins. Quarrels do not justify severing ties unless their connection causes harm to your religion or your worldly life.