Does a divorce take place if the wife says to her husband: "I will leave Islam and enter the the Jewish religion if I remain your wife"?

This utterance does not entail apostasy or affect the marital bond; the bond remains between the spouses. Ibn Abi Zayd al-Maliki stated in "Ar-Risala" that whoever says, "I have associated partners with Allah, or he is a Jew, or a Christian if he does such and such," is not liable for anything except seeking forgiveness. As for whether an expiation for breaking an oath is necessary if one reneges, there is a difference of opinion, and the more cautious approach is to offer expiation. It is advised to be wary of anger and for each spouse to respect the other and handle matters calmly.