What is the religious ruling on a wife remaining in the home of her husband who has children from a Jewish woman, and is this considered right or wrong on her part? What is incumbent upon her to do?

You did well by not aborting the pregnancy, and your patience with your husband is commendable. What your husband is doing, in terms of abandonment and wickedness, is not permissible for him. However, the Sharia does not obligate you to leave him, but it gives you the right to seek divorce or khul'. Your continuation in the relationship is left to your decision, with patience and supplication, or ending the relationship, especially if you are young and fear for yourself. Do not despair of advising him and reminding him of Allah. If he does not abandon adultery, it is not advisable to continue with him in the marital relationship due to its negative health and behavioral effects on the family.