Wa `alaykum as-Salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear brother, thank you for your question that shows concern to change your lifestyle to the better.
Indeed, a Muslim is highly recommended to guide people, especially wives and kinships, to virtue and piety rather than abandoning them.
Therefore, you are required to lead your wife to virtue, as you had shared her in the previous bad experience.
In his response to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
The fact that you had lived a life of sin prior to your marriage does not render your marriage automatically invalid, neither the fact that your wife is neglectful of her prayers.
Since you had been partly responsible for her to lead a sinful life, now that you have felt remorseful should not make you feel self-righteous and look down on her. Rather, you may do well to feel sorry for her condition and try your best to save her; this is best done through understanding and encouragement more than through coercion, intimidation, or threat of divorce. The Prophet (peace and blessings of Allah be upon him) taught us to show mercy towards those who are exposed to tests.
Therefore, it is better in this case for you to be instrumental in guiding your wife to Islam rather than abandoning her. Your marriage is still valid even though you doubt whether she has repented. I understand she is not persisting in sins. Both of you sinned, and both of you need to repent and beg for the mercy of Allah. Prayer indeed is the most fundamental pillar of Islam; it is your responsibility now, even as you have encouraged her to sin, to lead her on to a life of virtue. Remember the words of the Prophet (peace be upon him), “Should a single person be guided to the straight path through your efforts that would be even better for you than possessing the best of wealth.” (Al-Bukhari and Muslim)
May Allah make us all instruments of virtue and piety and locks to evil and corruption, amen.
Allah Almighty knows best.