Is the mother's anger considered religiously (sharan) valid in this case, and will her satisfaction be a sword wielded as she wishes, especially given that the father passed away pleased with the questioner and praying for him, and that the reason for the isolation is the widespread reprehensible acts among the siblings and the mother's unwillingness to accept advice?

It is recommended to supplicate for guidance and righteousness for one's siblings. Honoring one's parents is among the greatest acts of obedience, and Allah has given special injunctions concerning the mother. The Sunnah has allocated three-quarters of this righteousness to her. If the mother becomes angry without a valid Shar'i (Islamic legal) reason, then obedience to her is not absolutely obligatory. Furthermore, it is necessary to advise siblings with kindness and gentleness.