When Talaq Is Not Valid
Question

I have a request for clarification on an issue between my wife and me. My wife and I had a big argument after she had just completed her menses. Following her menses, we engaged in sexual activity on two consecutive days and then on the third day we had a very big argument and I said the word "Talaq" to her 3 times in one sitting. 
Out of ignorance, my understanding was that to give one divorce I was required to say it 3 times. My intention was not to divorce her 3 times but once only. Also since I engaged in sexual activity with her post her menses, is the Talaq valid or not? 
We both want to reconcile. I have read on some resources that saying the word "Talaq" 3 times in one sitting counts only as one and we can therefore reconcile and I have also read that if I divorce her post menses and have engaged in sexual activity with her during this period of purity then the divorce is not valid. 
This matter is causing us and our families a lot of stress and heartache and we also have three children to think about. Could you please provide some guidance on this situation and issue me a fatwa?.
Praise be to Allah.What is innovated divorce? 
If a man divorces his wife during a period of purity in which he has had intercourse with her, this is an innovated divorce (talaq bid‘i) and is haram. The Sunnah way of divorce means issuing one divorce (talaq) during a period of purity in which he has not had intercourse with her, because Allah, may He be exalted, says (interpretation of the meaning):
“O Prophet (blessings and peace of Allah be upon him)! When you divorce women, divorce them at their Iddah (prescribed periods), and count (accurately) their ‘Iddah (waiting periods).” [at-Talaq 65:1]
Al-Khatib ash-Sharbini (may Allah have mercy on him) said in his Tafsir (4/310): “That is, at the time when their ‘iddah (waiting period) can properly start.”
That can only be during a period of purity in which he has not had intercourse with her.
Does innovated divorce count?
The fuqaha differed as to whether this innovated divorce (talaq bid‘i) counts as such. The majority are of the view that it does count as such. Some are of the view that it does not count as such, including Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him). He was followed in that by a number of scholars.
It says in Fatawa al-Lajnah ad-Daimah (20/58): “The innovated divorce (talaq bid‘i) is of several types, such as when the husband divorces his wife during her menses, or nifas (postpartum bleeding), or during a period of purity in which he has had intercourse with her. The correct view is that this does not count as a divorce.”
Based on that, if you divorced your wife during a period of purity in which you had had intercourse with her, it does not count as such.
Triple divorce
The fuqaha differed concerning the threefold divorce .
The more correct view is that triple divorce counts as a single divorce (talaq), regardless of whether he said it in a single phrase, such as saying “You are thrice divorced”, or he said it in three separate phrases, such as saying “You are divorced, you are divorced, you are divorced”; and regardless of whether that occurred in one sitting or on several occasions between which he did not take her back or make a new marriage contract with her. This is the view favoured by Shaykh al-Islam Ibn Taymiyah and deemed more likely to be correct by Shaykh Ibn ‘Uthaymin (may Allah have mercy on him).
They quoted as evidence the report narrated by Muslim (1472) from Ibn ‘Abbas (may Allah be pleased with him) who said: At the time of the Messenger of Allah (blessings and peace of Allah be upon him), Abu Bakr and the first two years of ‘Umar’s caliphate, a threefold divorce was counted as one. Then ‘Umar ibn al-Khattab said: People have become hasty in a matter in which they should take their time. I am thinking of holding them to it. So he made it binding upon them.
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said: 
“The correct view concerning all these issues is that there is no such thing as a threefold divorce, unless it is three divorces in between which the husband takes the wife back or makes a new marriage contract with her; otherwise it does not count as three divorces. This was the view favoured by Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him), and it is the correct view.” (Ash-Sharh al-Mumti‘, 13/94)
Thus it should become clear to you that a divorce issued during a period of purity in which the husband had intercourse with his wife does not count as such. Based on that, no such divorce is to be counted in your case.
And Allah knows best.