What should the questioner do regarding his current wife who is cheating on him? And what should he do regarding his two children from his first marriage? And how can he maintain prayer and keep away from the unlawful?

Adultery is one of the most heinous major sins, and it entails punishments in this world and torment in the Hereafter. Whoever has committed this sin must offer sincere repentance and keep away from its causes. Allah accepts the repentance of sinners. Children born of adultery are not attributed to the father, and he is not obligated to any rights or duties towards them, but it is permissible to show kindness to them. As for the wife who has repented and become righteous, it is permissible to keep her in the marriage; otherwise, it is not permissible due to the effeminacy (dayouthah) involved. The husband must strive to invite his wife to goodness and to firm her upon righteousness, for he is responsible for her. Steadfastness and adherence to religion are achieved by asking Allah, performing many supererogatory acts of worship, and accompanying the righteous.