What is the ruling regarding a husband remaining with his wife who abandons prayer, claiming she is not convinced by it, especially since they have children together, and what is he obligated to do?

The husband must command his wife to pray and go to great lengths in advising her. If she does not comply, he must divorce her. He must also command everyone over whom he has authority to do so, acting upon Allah's saying, "And enjoin prayer upon your family [and people] and be steadfast therein" and "O you who have believed, protect yourselves and your families from a Fire." If the wife insists on abandoning prayer, the husband must divorce her. If she does not acknowledge the obligation of prayer or refrains from performing it out of disdain, she is, by scholarly consensus, a disbeliever, and it is not permissible for her to remain his wife.