Must the questioner divorce his wife who no longer obeys him, describes herself as not following the Sunnah of the Prophet, and whose behavioral problems persist, or not?

One of the greatest means of success in marriage is to seek a woman who is religious and of good character, by asking trustworthy people about her, and then performing Istikhara (seeking guidance from Allah). Marrying a woman without verifying her condition, especially if she has admitted to committing indecency and it is unknown whether she has repented or not, is a grave error. Since the aforementioned wife is negligent in her religious duties and of bad character, she should be divorced, because keeping her brings no good. Ibn Qudamah stated that divorce is recommended when a woman neglects Allah's rights, and he cited the Hadith: "There are three whom Allah does not answer: a man who had a wife of bad character but did not divorce her," because the man tortures himself by living with her while he has the means to separate from her.