الجواب وبالله التوفيق

As per the situation described in your question the wife has become mughallidha due to the three issued divorces which all took effect, living together with your wife without performing Shar‘ai Halalah is impermissible. The divorce issued while in the state of anger takes effect just as it takes effect while issued in a state of calmness. Usually divorces are issued while people are in the state of anger. By writing the divorce three times and verbally issuing it three times, the three divorces have taken effect.

یقع طلاق کل زوج اذا کان بالغاًعاقلا ًسواء کان حراًاو عبدا ًطائعاًاو مکرھا (فتاویٰ محمودیہ، ص149، ج18

وقال ابو داؤد الطلاق اظنہ فی الغضب ۔

The divorce issued while the wife is in the state of menstruation still takes effect according to the Islamic Shari‘ah, although it is against the preferred way to issue a divorce during that period.

واذا طلق الرجل امرتہ فی حالت الحیض وقع الطلاق (حاشیہ فتاویٰ محمودیہ ص 47، ج18

It is impermissible to perform a new Nikah with her without performing a Shar‘ai Halalah. Allah Subhanahu Wa Ta‘ala says in the Holy Quran:

فَاِنۡ طَلَّقَهَا فَلَا تَحِلُّ لَهٗ مِنۡۢ بَعۡدُ حَتّٰى تَنۡكِحَ زَوۡجًا غَيۡرَهٗ ‌ؕ (البقرۃ 230

If a new Nikah has already been performed, it will not be considered correct and the man and women should immediately separate.

کذا فی کتب الفتاویٰ

واللہ اعلم  بالصواب