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 is His slave and Messenger.
We congratulate you upon embracing Islam and it is a blessing that requires thanking Allaah. Your efforts to be a good Muslim woman are a perfect act of being thankful to Allaah on this blessing. We ask Allaah to make you firm on the truth and guide you to wisdom. We welcome all your questions and queries with great joy.
The answer to your question is that the consent of the guardian of the woman is a condition for the validity of the marriage contract. So, if you were from the People of the Book at the time of your marriage and a person from your religion married you off or you were Muslim and you authorized a Muslim to marry you off, then you become the wife of this man. Therefore, you deserve all the rights as a wife from her husband such as bridal money, expenditure, etc. Delay in documenting your marriage does not affect the validity of the marriage, and it is not even a condition for the validity of the marriage. See Fataawa 83157, 88488 and 83629.
On the other hand, if this marriage was conducted without the consent of your guardian then it is invalid and should be cancelled but these two children are traced back to their father due to the controversy regarding the ruling of this marriage. They have the same right on their father as his other sons have upon him. So, it is not allowed for him to disown them, and must shoulder their responsibility.
Finally, your husband must spend his nights justly between you and your co–wife, as long as you did not give up this right. The scholars have clearly mentioned that a wife has the right to ask her right back if she has waived it in the marriage contract. For more benefit, please refer to Fataawa 84411 and 90689.
Allaah Knows best.