He divorced her for the third time and is saying that the first divorce was during a period of purity in which he had intercourse with her

The sunnah with regard to divorce (talaaq) is that the man should divorce his wife during a period of purity (i.e., when she is not menstruating or bleeding following childbirth) in which he has not had intercourse with her. If he divorces her during the period of purity in which he has had intercourse with her, it counts as a divorce according to the majority of scholars. 

But some scholars are of the view that this is an innovated divorce (talaaq bid‘i) and does not count as such. 

If a man gives his wife an innovated divorce and counts it as such, based on his own opinion or following the opinion of the majority of scholars, or following the opinion of one who gives a fatwa concerning that, then his divorce is valid and counts as such, and he does not have the right, if he divorces his wife for a third time, to re-examine the previous divorce for the purpose of taking her back, because this is a kind of haraam trickery, and his wife does not become permissible to him by means of that. 

Dr. Ahmad ibn ‘Abd al-Rahmaan al-Qaadi (may Allah preserve him) said: 

I asked our shaykh, Shaykh Ibn ‘Uthaymeen: A man took his wife to her family’s house with the intention of divorcing her, but when he met her father he was reluctant to utter the word of divorce clearly, and he said: “It seems that we are finished” or words to that effect. That was during a period of purity in which he had had intercourse with her. Is she divorced? 

He replied: This phrase was accompanied by the intention (of divorce) and so it counts as a divorce. With regard to it being during the period of purity in which he had had intercourse with her, or divorcing during the menses, my way of issuing a fatwa is: 

If the question comes when the woman is still observing ‘iddah, I tell the questioner that it does not count as a divorce, as is the more correct view. If the question comes after the end of the ‘iddah, I tell the questioner that it does count as divorce, as it is the view of the majority that an innovated divorce counts as such, and because the husband believes that she is no longer married to him, and if she married another man after the ‘iddah, he would regard it as something valid. 

Then he said: I asked our shaykh (may Allah have mercy on him) about a man who divorced his wife three times and his wife told him that the second time he divorced her, she was menstruating. Is she irrevocably divorced from him? 

He replied: I ruled that she is irrevocably divorced from him, because when he divorced her, he did so on the basis that it was the final divorce and people did not regard the divorce issued at the time of menstruation as anything other than a divorce, and they did not regard the threefold divorce as one divorce until the fatwa of Shaykh ‘Abd al-‘Azeez ibn Baaz to the contrary became widely known. Then the one whose wife became irrevocably divorced from him started saying, One of them was done in a moment of extreme anger, and the other one when she was menstruating and so on, to avoid it being counted as divorce.  

Then Dr. al-Qaadi said: I discussed this matter with the shaykh as did other brothers, because we know that he did not regard the innovated divorce as valid, but he insisted on the fatwa mentioned above which states that the divorce in this valid was valid and counted as such. 

End quote from Thamaraat al-Tadween min Masaa’il Ibn ‘Uthaymeen

Based on that, you have divorced your wife three times. 

And Allah knows best.