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.
If this divorce had truly taken place, like if the husband uttered the words of divorce for example, or that he wrote the words of divorce while intending it when writing it, then such mistakes in the papers of divorce does not prevent divorce from taking place, in this case, divorce is effective.
Moreover, having witnesses for divorce is desirable but not an obligation according to the most preponderant opinion of the scholars . For more benefit, please refer to Fatwa 89894.
As regards those children, then she may take their matter to an Islamic judge or to an authority that acts on his behalf in non-Muslim countries, like the Islamic centers and the like.
Finally, if this is not the third divorce, the husband is permitted to take her back without a new contract as long as she is still in her waiting period. If her waiting period expired, he cannot take her back except with a new marriage contract, a new dowry and the consent of her guardian. For more benefit on the kinds of divorce, please refer to Fatwa 82541.
Allaah Knows best.