Is it permissible for a brother who is harmed by his sister and slandered by her lies to go to Hajj and suffice with greeting her, without visiting her in her home, in order to avoid her harm, and is his Hajj valid in this case?

It is regrettable to witness strained relations among relatives, allowing Satan to sever kinship ties. He spreads hatred among loved ones and rejoices in their separation, as mentioned in Surah (definition) Al-Isra (17:53) and in a Hadith (definition) by Muslim concerning Iblis. It is advisable to use one's intellect and strive for reconciliation due to its great virtue, as stated in Surah An-Nisa (4:114) and in the Hadith by Abu Darda: "Reconciling disputes is better than fasting, prayer, and charity." Whoever fabricates a lie has committed an injustice. Such a person should be advised and reminded of Allah with wisdom. If they do not heed the advice, it is permissible to ostracize them as a deterrent, or to continue interacting with them based on what serves the Islamic interest. The reconciliation or estrangement of the husband with his wife's sister does not affect his Hajj, nor is he obligated to go bid her farewell before Hajj; a phone call is sufficient.