Is a new mahr required for the wife after the 'iddah has ended and her family has refused to return her, and is her maintenance obligatory in this case, and is she still considered to be within the marital bond after an attempt was made to bring her back and her family refused during the 'iddah?

There should have been no haste in divorce merely due to a quarrel, especially with the presence of children. If this divorce is considered a revocable divorce, then the husband has the right to take his wife back even if her family disapproves or she herself does not wish to, based on the Almighty's saying: "And their husbands have a greater right to take them back during this period, if they wish reconciliation." Her family erred by refusing her return without a valid reason. The return (revocation) is not effected merely by her coming to her family; rather, it must be done through legitimate means. If the waiting period (iddah) expires without a return, she becomes a stranger to him, and he cannot take her back except with a new contract and dowry. She then has the right to refuse to return to him, as he becomes one of the suitors. As for maintenance during the waiting period, there is no maintenance for the disobedient wife (nashiz) if she refuses to return. It is advised to seek the arbitration of wise people when necessary.