All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, we thank and praise Allaah Who guided you to Islam and we ask Him to make you firm and steadfast on His Religion until the day you meet Him.
We advise you to seek beneficial knowledge, perform good deeds and befriend righteous and pious women, as this is one of the best things that help a Muslim woman remain steadfast on her religion.
As regards your question, according to the preponderant view of the scholars the presence and consent of the guardian is one of the conditions for the validity of marriage. If the woman is from the people of the Book, then a guardian from her religion would marry her off as we clarified in Fatwa 92039. [As then you were still not a Muslim]
Therefore, if the marriage did not take place with the consent of your guardian, then it is a void marriage and it must be invalidated, and your two children should be traced back to their father as he married you believing that the marriage contract was correct. For more benefit, please refer to Fatwa 90689.
Then, if you wish to renew the marriage contract, you may renew it with the consent of your [Muslim] guardian and two witnesses. If you have no Muslim guardian, then you may appoint a Muslim man to conduct your marriage contract and marry you off.
Allaah Knows best.