What is the ruling on remaining with a husband who is addicted to the internet, flirts with both sexes, has promised them to commit sodomy, and sends them money, despite his regular attendance at prayers and the mosque?

You are permitted to stay with your dissolute husband as long as he remains a Muslim. However, it is advisable not to despair of counseling him and to strive for his reform, assisting him towards repentance. If he does not repent and persists in his disobedience, it is better to separate from him through divorce (talaq) or khul' (judicial divorce initiated by the wife). It is commendable for a woman to seek khul' from him due to his abandonment of the rights of Allah Almighty.