How is the marriage contract established between a Christian husband who has converted to Islam and his Muslim wife who has abandoned prayer, when they also have children?

If a woman completely abandons prayer, she is an apostate. If she prays sometimes and abandons it sometimes, she is severely disobedient (fasiqah).

The marriage of a Muslim woman to a disbeliever is invalid by the consensus of Muslims, due to the Almighty's saying: "And do not marry [your daughters] to the polytheists until they believe."

It is obligatory to annul this invalid marriage. If the woman repents and her waiting period (iddah) from the invalid sexual intercourse expires, then the man may marry her anew.

Some scholars are of the view that the marriage should be upheld if both spouses embraced Islam after the marriage of an apostate woman to a disbeliever, such as Ibn Taymiyyah, who held that their marriage should be upheld.

However, it is more prudent for the woman to separate from the man, repent to Allah, and then marry him anew after her waiting period expires.