Is donating money with the intention of charity on behalf of the deceased mother and the rest of her family, who were insulted in a moment of anger, sufficient to atone for the sin, or is something else required?

Abusing the dead is forbidden and reprehensible, and it is worse than abusing the living, because it is not possible for the dead to grant forgiveness. Therefore, whoever has done this must repent with a sincere repentance, seek forgiveness from the living, seek forgiveness and supplicate for the deceased, perform many righteous deeds, strive for reconciliation, and know that giving charity on behalf of the dead is a good act and benefits the deceased.