All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Firstly, you should know that you bear no sin for merely having divorced your wife. You rather did the right thing by divorcing her because she refused to adhere to righteousness and obedience to Allah, The Exalted, observe the Islamic Hijaab, and avoid prohibited intermixing with non-Mahram men. In fact, it is recommended to divorce such a wife. Ibn Qudaamah said in Al-Mughni when talking about the rulings of divorce: “The fourth case (of divorce) is desirable, which is when the wife is neglectful of the obligatory rights of Allah, The Exalted, over her, such as the prayer and the like, and he (her husband) cannot force her to fulfill them, or when his wife is not chaste...” [End of quote]
This woman has done evil by committing Zina (fornication), and it is obligatory on her to repent to Allah, The Exalted. If it becomes clear to you that she has repented sincerely, you may take her back in marriage, conceal her sin, and live with her in kindness. In this case, you should strive to forget about her sin and remember that she has repented and become upright and that Allah, The Exalted, forgives for the repentant, his serious sins and that He is the Creator and Bestower of blessings, and therefore the slaves of Allah should forgive the offender with greater reason.
We here point out that it is impermissible for you to take her back in marriage after the expiration of her ‘Iddah (post-divorce waiting period) except with a new marriage contract unless it was the third occurrence of divorce. After the third occurrence of divorce, a woman becomes unlawful to her husband to take her back in marriage until she marries another man – a marriage that is based on mutual desire – then the new man happens to leave her on account of divorce or death. Allah, The Exalted, Says (what means): {And if he has divorced her [for the third time], then she is not lawful to him afterward until [after] she marries a husband other than him…} [Quran 2:230]
Allah Knows best.