What should I do with my wife, who is negligent in prayer, after I have advised her and threatened her with marriage, all to no avail, so that it benefits me in my religion and guides her?

Allah Almighty made man the guardian over woman; he is responsible for her discipline, protection, and preservation. The husband must enjoin his wife to do what is right, foremost among which is prayer, an individual obligation upon her. If the husband exerts his utmost in advising her and she persists in neglecting Allah's right, he should forsake her in bed, then strike her with a non-bruising strike. If that does not help, then separating from her is better than living with her, because meeting Allah Almighty and her sincerity in His accountability are better than living with a woman who does not pray.