What is the ruling on estrangement from one's parents and their intense anger towards their son and his wife, and what should the son do to appease them, despite his continuous attempts at reconciliation, and his claim that they are harsh and refuse to forgive him?

Filial piety towards parents and maintaining kinship ties are both obligatory, and the mother's right is greater. You have committed a great wrong by severing ties with your mother for an entire year, as that is an act of disobedience (ʿuquq) and one of the gravest major sins. You must hasten to repent to Allah, strive to show piety towards your mother, seek her رضا (pleasure/contentment), and be patient in doing so. You must also maintain ties with your siblings with kindness, even if they treat you poorly. If they refuse and insist on severing ties, then the sin of that will be upon them.