Is my obligation for my wife's mahr (dowry) absolved after divorcing her, if the families agree not to demand anything?

If the party is the woman’s guardian or agent, and they release you from what you owe in exchange for her divorce due to her recalcitrance (nushuz), then the Mahr (dowry) is waived for you. However, if the recalcitrance is from your side, you are not entitled to take compensation for her divorce; rather, you must relieve her of harm, either by keeping her honorably or divorcing her without compensation. It is not permissible for you to keep her in order to take money from her, based on the Almighty’s saying: "And do not prevent them from marrying [others] to take [back] part of what you had given them, unless they commit a clear immorality. And live with them in kindness. For if you dislike them - perhaps you dislike a thing and Allah makes therein much good."