They were able to hear and see one another, except for the wife; they could only hear her voice. There was no deceit involved in this matter. The wife follows the Maaliki madhhab and the husband follows the Hanafi madhhab.
The wife, who was a divorcee, appointed one of the two witnesses to give her in marriage by saying: I appoint So-and-so to give me in marriage to So-and-so – namely her husband. That was in their presence of my father and with his agreement.
At that point, the guardian asked the husband: Do you accept marriage to So-and-so? And he replied: Yes.
After that the contract was registered with the appropriate authorities, and there was a waleemah (wedding feast). In other words, the marriage was publicized before consummation. A little girl was born as a result of this marriage. Is this marriage contract valid?
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
It is valid to conclude the marriage contract via video call as long as the conditions of marriage are met.
Answering your question, the Fatwa Center at Islam Q and A, states:
In order for the marriage contract to be valid, it is stipulated that it should be done by the guardian (wali) of the woman or his proxy. The woman should not do the marriage contract or appoint a proxy for it. This is the view of the majority of scholars with the exception of the Hanafis.
The marriage contract that is done by a proxy appointed by the woman to do it on her behalf is only valid according to the Hanafi madhhab.
So long as the marriage contract was done according to an established madhhab, it is not to be invalidated, especially since it is known in this case that the father agreed to the marriage and was in fact present when the marriage contract was done.
In order for the marriage contract to be valid, it is essential that the marriage contract be witnessed by two Muslim witnesses, and it is not valid for the guardian (wali) to be a witness.
It says in Sharh Mukhtasar Khaleel by Al-Kharashi (3/168):
“It is not permissible for the wali to be a witness to the marriage contract of the woman under his guardianship, even if there is someone else with him (as a witness).”
However, the testimony is not limited to those who are asked to be witnesses and sign the official papers; rather anyone who is present when the marriage contract is done and is fit to give testimony is a witness.
Based on that, the imam of the mosque in this case may be considered a second witness, and the marriage contract is valid; it does not matter that he was acting as registrar.
Moreover, it is valid for the brother of the wife to be a witness to her marriage; there is a difference of scholarly opinion as to whether it is valid for her father to also be a witness.
In conclusion, the marriage contract of your sister is valid and the daughter of your sister is a legitimate daughter.
Almighty Allah knows best.