All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
If this woman converted to Islam and her husband remained non-Muslim, then her marriage has become invalid. In case her husband embraces Islam while she is still in her waiting period ('Iddah), then he has more rights to her than any other man (i.e. she remains his wife). However, if her waiting period has expired, then he has no right to her and she can marry another man. For more benefit, please refer to fatwas 107894 and 84226.
Therefore, if she deserted her husband because of embracing Islam, then she has the right to do so, but it is not permissible for her to desert her children.
The children who are below the age of puberty are ruled to be Muslims because of following their mother, as the children follow the best of the parents in regard to religion, as we have already clarified in fatwa 81957. The father has no right for custody of the child who has not reached puberty, so she is obliged to strive to take the child from their non-Muslim father.
If this woman follows the Nation of Islam, then it is an obligation to clarify the true religion to her in a gentle and soft manner and to advise her about the evil thoughts and false beliefs of the Nation of Islam. It is more appropriate that trusted Muslim scholars in your area clarify this matter to her. You may also make use of what has been mentioned in fatwa 83361.
Finally, it should be noted that it is not permissible for a Muslim woman to have a relationship with a man out of wedlock, but there is nothing wrong for that woman to try to terminate her relationship with her husband who did not embrace Islam so that she can get married to a Muslim man.
Allah knows best.