Should the mother go to reconcile with the father who abandoned the home due to disputes, even though he is in the wrong and accustomed to abandoning the home, and threatens to marry another, knowing that he does not acknowledge his mistakes nor does he defend his daughters?

The relationship between spouses is based on living together in kindness. In case of disagreement, the prescribed course of action is to attempt reconciliation by admonishing the wife, then forsaking her (in bed), then striking her (lightly), and if these do not work, then sending two arbiters. The father abandoning the home without a legitimate Shariah reason is not permissible, and reminding him of past disagreements is not beneficial. As for his right to conjugal relations with his wife, it is established, and the wife must obey him. The mother forgiving her husband's mistakes and going to reconcile with him is among the virtues of good character and forgiveness that Allah loves.