What is the ruling on abandoning a wife who persists in disobeying her husband and engaging in illicit relationships, and is the husband sinful for doing so?

Turning the wife over to her family's house is not a permissible form of desertion.

Regarding the conditional divorce, it does not take effect as long as the wife denies the writing, unless her falsehood becomes evident.

It is advised to return the wife to the home and treat her kindly, cooperate in obedience to Allah, and prevent her from visiting her family if there is fear of them corrupting her.

If the means of reconciliation do not work, then divorce is the last resort.