Praise be to Allaah.
Praise be to Allaah Who has guided them to Islam. We ask Allaah to help us and them to be steadfast in adhering to His religion. In response to your question, if the marriage was contracted through an offer or proposal (eejaab) from the walee (guardian) of the bride and acceptance (qabool) on the part of the groom, with the consent of the bride, in front of two Muslim witnesses of good character (as regards piety, attitude, conduct, etc.), then the marriage contract is valid. Ibn Qudaamah (may Allaah have mercy on him) said: “A marriage is not properly contracted unless there are two Muslim witnesses, regardless of whether the bride and groom are both Muslims or only the groom is. This is what Ahmad stated, and it is also the opinion of al-Shaafi’i.”(Al-Mughni, 9/349; al-Mufaddal fi Ahkaam al-Mar’ah, 6/120).
If the marriage was conducted as described above, then it is valid, otherwise it must be repeated. It is permissible for a non-Muslim woman to be married by her non-Muslim guardian, but if she becomes Muslim, this role can only be played by a Muslim. If she has no Muslim walee, then this role can be delegated to the director of the Islamic Centre or whoever is acting in his stead. As regards the children who were born during this time, they are the children of the man and should be given his name, as is the ruling in cases where there is uncertainty of this nature.
And Allaah knows best.