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
Question

                I had divorced my wife in the time of purity which we had physical marital relationship / had sexual intercourse. And after few weeks she travelled going to her home country and before travelling she asked me to write her a paper to confirm her divorce, which I did write and when she was in her home country she went to a court and made an official divorce certificate. After a period of almost six months she returned to the country where I was and we meet and re-marry again and after one year of being in marriage we divorced again and re-marry again after one year of our second divorce and now we are divorced again for the third time after being in marriage of the third period for more than four years. But we heard that our first divorce is totally laying in the category of Talaq bidaa, because I divorced her in the purity which we had a physical marriage act (sexual intercourse) which according to some Islamic scholars is not counted as a valid divorce (talaq).

We both love each other but circumstances drive us where we are today (apart) and we have three children together of the age between 1.5yrs and 8.5yrs.We believe we have realize our mistake.

Do we have the opportunity of being together before the woman being married by another man?

- Can we be wrong (doing haram) to follow the explanation of those scholars whom consider the divorce pronounced in an unclean purity void/invalid and re-marry again?

- And if the first one was not valid can we say that all are invalid since we start to count from one and not two (as the second one was due to the outcome of the first one).

- If the first divorce was not valid is it necessary to re-marry her or can I just consider it did not happen and say we are still married.
Please help me and I need your advice in this matter.
Praise be to Allah.
      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.