Is it legally and religiously permissible for a husband to ask his wife to write a documented legal and religious confession that she falsely accused him, given that she accused him of assault, constantly threatened him, insulted him and his family, and left the marital home without his permission, despite his repeated attempts to send her on trips abroad? What is the religious and legal advice for the husband in this situation?

Your wife is unjust and rebellious, as indicated by her slander and false threats against you, her leaving without your permission, and her cursing you and your parents. She forfeits her right to maintenance (nafaqah), clothing, and equitable division (qasm). Her treatment should be as commanded by Allah in verse 34 of Surah An-Nisa. If she does not respond and the relationship deteriorates, and mediators are unable to help, then there is no blame upon you for separating from her and divorcing her. The advice here is to separate from her; her harm has extended to your parents, and it is mentioned in a noble Hadith that the supplication of one who does not divorce a bad-tempered wife will not be answered, because he is tormenting himself, and he has the capacity to separate from her. As for seeking to uphold justice and remove oppression, there is no harm in it Islamically.