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.