They committed zina and got married before they repented; do they have to do a new marriage contract?
Question

                A young Muslim man got married three years ago to a girl who only embraced Islam a week before the wedding, and now they have a child and she is six months pregnant with their second child. But before they got married they were in a haraam relationship and they committed immoral actions several times. Now it seems to them, after reading a fatwa, that their marriage is invalid and that it must be annulled as they did not repent before marriage. In fact they only repented after marriage.

What should they do now? Do they have to annul their marriage now and then repeat it without any need for ‘iddah? Does this mean that their children are the result of haraam and immoral actions (are they illegitimate)? Do they come under the ruling on zaanis (fornicators) for the duration of their marriage? Is annulment a straightforward procedure, or is it a lengthy process like talaaq (divorce)? Can they be excused because of their ignorance? All they want to do is live a clean married life that is pleasing to Allah, may He be blessed and exalted. Please note that the girl got her period once before they got married and the young man did not have intercourse with her after that until after they got married; that is, he wanted to make sure that she was not pregnant before marriage. Allah knows that they did not know that repentance is stipulated as a condition of marriage being valid, otherwise they would not have hesitated to repent straightaway at that time. What about the children, do they not deserve some consideration in this situation? Can they stay together for the sake of the children only, without any sexual intimacy? I tried to find out about the matter as much as I could so that all aspects of it would be clear, because they found two contradicting opinions that only increased their confusion, and they do not know which way to proceed. They do not want to live in haraam and they hope that you can explain with detailed evidence.
Praise be to Allah.
    Firstly: 

    It is not permissible for the zaani 
    (fornicator or adulterer) to marry the zaaniyah (fornicatress or adulteress) 
    except after repenting because Allah, may He be exalted, says 
    (interpretation of the meaning):

    “The adulterer marries not but an 
    adulteress or a Mushrikah and the adulteress none marries her except an 
    adulterer or a Muskrik. Such a thing is forbidden to the believers (of 
    Islamic Monotheism)”

    [an-Noor 24:3]. 

    Repentance is achieved by regretting (what 
    one has done) and resolving not to go back to the sin. This may have 
    happened in the case asked about here, hence they gave up zina and wanted to 
    live a clean life that is pleasing to Allah, as you say, and they wanted to 
    be on the safe side by making sure that she was not pregnant as a result of 
    something haraam. 

    The fuqaha’ differed concerning the validity 
    of a marriage between two who committed zina, if the marriage was done 
    before they repented. The majority are of the view that it is valid, but the 
    Hanbalis are of the view that it is not valid, and this is the more correct 
    view. See question no. 85335 

    What is required in that case is to repeat 
    the marriage contract. The matter does not require a talaaq (divorce); 
    rather it is a repeat of the marriage contract, in which the woman’s wali 
    (guardian) may be her Muslim father, brother or any other male relative on 
    the father’s side, so long as he is Muslim. If she has no male Muslim 
    relatives, then the imam of the Islamic Centre may act as her guardian for 
    the purpose of marriage, in the presence of two Muslim witnesses. 

    It is not essential to tell the one who does 
    the marriage contract of the details of the situation; it is possible to use 
    double entendres and to say that they want to repeat the marriage contract 
    because of some uncertainty about its validity, because they got married 
    without a wali, or for some other appropriate reason, or because it was done 
    in another city or country, and so on, because the Muslim is enjoined to 
    conceal his faults and mistakes. 

    Secondly: 

    The children who were born under the 
    previous marriage contract should be attributed to the husband, because they 
    were born in a marriage that both spouses believed to be valid. 

    And Allah knows best.