Do the sisters' actions of expelling their brothers' wives from the house after their quarrel on the day of their mother's death, and refusing to go to the elder brother's house to apologize to his wife, who had been stubborn with their mother, constitute a mistake that warrants the elder brother's anger?

You must remove the animosity and estrangement between you and your brother, for believers are brothers, and you are bound by ties of kinship that Allah has commanded to uphold. Apologize for what transpired from you towards your brother's wife. Good-hearted people can mediate to reconcile between you. A brother's wife is a stranger [non-mahram], so interaction with her must adhere to শরী'আ-compliant regulations.