Does a petitioner prevent good and sever ties of kinship if he insists on his refusal to his brother's marriage to a woman with whom he was in contact and whose family stipulates his approval, knowing that she was married or in her 'iddah during their contact?

A revocable divorcee is considered like a wife, so it is not permissible to hint at proposing to her. Whoever instigates a woman against her husband is committing something forbidden and a major sin, based on the Prophet's (peace be upon him) saying: "He is not of us who instigates a woman against her husband." Some scholars have gone as far as to invalidate the marriage of the instigator. Your brother must repent. If the woman repents and your brother repents, and there is no way for her to return to her former husband, then there is no objection to him marrying her.