What is the religious ruling and the view of the religion regarding a situation in which the mother accuses her son's wife of not handing over a sum of money sent by the son, while the wife swears that she did hand it over, so how can this situation, which led to the mother's anger and her continuous recalling of the incident, be dealt with?

What you have done is correct, which is to find excuses for your mother and your wife, for forgetfulness is common, and the insistence of each of them on what she predominantly believes to be true is something for which they are excused. Continue to be keen on reconciling them, for reconciling disputes is one of the greatest acts of closeness to Allah, as Allah the Almighty says: "No good is there in much of their private conversation, except for whoever enjoins charity or good or reconciliation between people." (An-Nisa: 114), and the Prophet, peace and blessings be upon him, said: "Reconciling disputes is better than the rank of fasting, prayer, and charity." Your brothers' criticism of you is incorrect, for it is not permissible for you to wrong your wife to please your mother.