The ‘iddah following divorce (talaaq) had ended and her husband had intercourse with her without being certain that he had taken her back during the ‘iddah
Question

                I request you to please let me know the sharia ruling with regard to my situation. Couple of days back I came across some fatwas / figh explanation from an Islamic forum regarding divorce which made me anxious with regard to my current married life. As a consequence of this, I decided to write to you and seek the correct position InshaAllah.
I have been married for over 15 years now. Except the past 7 months, I was always living and working alone in different cities / countries while my wife used to live with my parents at my home back in my home country. I used to periodically visit my parents once or twice a year for about 2-3 weeks. About 11 years back, I had issued a single divorce (1 time) to my wife in writing who was staying in my house with my parents while I was working in a different city. The family elders thought it wise to send her back to her fathers home while they were trying to resolve the issue and they sent her to her parents. Within couple of months my father passed away and I came home to visit my mother. At that time, I was told that my wife had returned to my house to support my mother. My reply to that was a single word "Okay". I do not know for sure if she returned during her iddat or after completion of her iddat period. Anyway, I was upset that she was returned without me revoking the talaaq. I never spoke to her, looked at her or touched her for over 1 year. 6-7 months fter this or so I decided to have sex with her as a result of emotional pressures. Though I was anxious at that time that this may be haram, I thought since I had not said talaaq 3 times this may be Okay. Since then, we continued to live like husband and wife whenever I visited home
During my research in the past few days, I now understand that since I had not revoked the talaaq before she completed her iddat, the talaaq had automatically converted into talaq-e-bain and our subsequent relationship has been illegal.
Could you please answer the following for me.
If my saying “okay” to being informed that she returned, happened before her iddah expired, can this be considered as having taken her back (though I had not considered it as revoking the divorce and did not have that intention at all)?
Is our current status a haram one? Is it like we have committed adultery? If yes, what is the way forward for me?
If you need any further details, please let me know.
Praise be to Allah.Firstly: 
If a man divorces his wife and this was the first or second talaaq, and the ‘iddah has not yet ended, he may take her back verbally, such as saying, “I take you back” or “I have kept you”; or it may be done by an action with the intention to take her back. If he has intercourse with her with the intention of taking her back, that also counts as taking her back. 
The ‘iddah of a woman who menstruates is three menstrual cycles; when she becomes pure following the third menses and does ghusl, then her ‘iddah has ended. 
The ‘iddah of a woman who does not menstruate because she is too young or has passed the age of menopause is three months. 
The ‘iddah of a woman who is pregnant ends when her pregnancy ends. 
Secondly: 
Your saying “okay” when you saw that your wife had returned to your mother’s house when in fact you did not want to cancel the divorce, and your staying for one year without approaching her or looking at her – all of that indicates that you did not actually take her back with that word, because you did not intend to take her back thereby. Rather it was approval and agreement with her being present to serve your mother. In that case the ruling does not differ whether that happened during the ‘iddah period or afterwards, because this word does not indicate taking her back. 
What happened of intercourse after that was a haraam action. You should have asked before that, especially since you felt anxious about what you had done. 
Based on that, what you have to do is repent to Allah for having intercourse when you did not believe that you had taken her back. And you have to do a new marriage contract – fulfilling all the conditions of the wali (guardian), mahr and two witnesses – if both of you want that. And it is not permissible for you to come near her until the marriage contract has been done, because she is a non-mahram to you. 
And Allah knows best.