Her brother is the only Muslim in her family, and he stubbornly refused to give her in marriage to someone, so they chose someone else to be her guardian

Praise be to Allah.

Firstly:

The marriage contract is not valid unless it is done by the woman’s guardian or his proxy.

The woman’s guardian should follow the same religion as her, and be her son, then her father, then her grandfather, then her brother, then the son of her brother, then her paternal uncle, then the son of her paternal uncle, in that order.

You stated that this brother of your wife is the only Muslim, then you stated that the family chose someone else to be a guardian for the girl. If that person is a disbeliever, then it is as if there is no guardian, and the marriage is not valid.

Secondly:

With regard to what you have mentioned about this man, and his asking whether you have your own house or your own business, we do not think that this is too much to ask. Rather this is something common that many people are keen to ask, in order to guarantee the interests of their daughter or sister.

With regard to the fact that he committed zina, if he has repented from it and rectified his affairs, then his right to guardianship is not waived.

But if he is persisting in unlawful relationships, or drinking alcohol, or being careless about prayer, then he is an evildoer, and the guardianship of an evildoer is a matter concerning which the scholars differed. The view of the Shaafa‘is and Hanbalis is that it is not valid, although most of the scholars are of the view that it is valid. This is the view of the Hanafis and Maalikis, and is the view favoured by Ibn Taymiyah and others.

See: Nihaayat al-Muhtaaj (6/238); al-Insaaf (8/73); Haashiyat Ibn ‘Aabideen (3/55); Haashiyat ad-Dasooqi (2/230); Minah al-Jaleel (3/289); Majmoo‘ al-Fataawa (31/101).

Thirdly:

If it is proven that he is an evildoer, or he used to harm the woman and did not seek her best interests with regard to marriage, or he prevented her from marrying someone who was compatible and with whom she was pleased, then his guardianship is waived and it passes to the next Muslim relative. If she has no Muslim relatives, then she may be given in marriage by the Muslim judge (qaadi). If there is no Muslim judge, then she may be given in marriage by the imam of the Islamic centre or jaami‘ mosque. It is not valid for her to give herself in marriage or for her to be given in marriage by a disbeliever under any circumstances.

If her marriage contract was not done by one whose guardianship is valid, then what must be done now is to repeat the marriage contract. If the brother agrees to undertake that, all well and good, otherwise it may be done by the imam of the Islamic centre, if she has no Muslim among her relatives who could give her in marriage.

And Allah knows best.