Wa `alaykum as-salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings.
Dear brother, thanks for your question. May Allah relieve your distress and help you lead a pious way of life.
When a person embraces Islam, he or she has to change his or her way of life and fully adapt himself to the teachings of Islam. Sometimes past mistakes have consequences that one cannot easily get rid of. However, even in these cases, a Muslim has to seek the Islamic remedy for his or her situation as there is no excuse for leading a sinful life under Islam.
Answering this question, the Permanent Fatwa Committee of the Assembly of Muslim Jurists of America (AMJA), stated,
You should do your best to keep away from what Allah prohibits. The one who tastes the sweetness of faith will always hate to go back to kufr (disbelief) just as he or she hates to be thrown into Hellfire. It is good that you realize that Islam does not permit sexual relationships outside marriage. Almighty Allah describes the believers as “Those who guard their private parts, save from their wives or those whom their right hands possess, for then they surely are not blamable” (Al-Mu’minun 23:5–6)
You should strive to call this woman to Islam. May Allah make you the cause of her following the truth, because then you and your son will be safe, and because of you Allah will save two souls from Hellfire.
However, if her conversion to Islam is not easy, you can marry her after making sure that she has repented committing adultery. Allah allows Muslims to marry Christian or Jewish women who are chaste. Hopefully, this might guide her to embrace Islam. At any rate, you should keep on striving to call her to Islam under all circumstances. Your relationship with her outside lawful marriage is prohibited, even under the circumstances that you mentioned.
Allah Almighty knows best.
Excerpted with modifications from www.amjaonline.com.