Does a mother sin for the severing of ties with her brother, despite her repeated attempts to end this estrangement, knowing that the noble Hadith states: "If two people sever ties for more than three days and one of them dies, he will enter the Fire, and neither his fasting nor his prayer will be accepted"?

If the mother has done everything in her power to end the estrangement and rift between her and her brother, then there is no sin upon her. The sin falls upon her brother for severing ties of kinship, depriving his sister of inheritance, not visiting her during her illness, and refusing to meet her. The brother must fear Allah and repent, and the sister must be patient, pray for him, forgive him, and continue her attempts to end the estrangement.