Is it permissible to inform a person of an offense committed in their absence, and is it permissible to harm the offender’s family in retaliation for their offense, and if that is not permissible, then what is the ideal solution?

It is not permissible to inform someone that another person has wronged them in their absence, as this constitutes backbiting (namimah). Nor is it permissible to wrong the family of someone who wronged your family, because this is an injustice and a wrongdoing against innocent people. A person is held accountable only for their own actions. Allah Almighty says: "And every soul earns not [anything] except for itself, and no bearer of burdens will bear the burden of another." As for your family, they may deal with those who wronged them in one of three ways: forgiveness and pardon, or withholding forgiveness so that the wrongdoer receives their due, or retribution and responding to a wrong in kind without transgression.