What is the religious ruling on taking back a wife after divorcing her three times due to her provocations and the coolness of feelings between the spouses?

"The question about a wife's nushooz (disobedience/rebellion) should have been raised at its onset, to allow for the situation to be remedied and corrected. Divorce was not the first solution. Regarding the three divorces: the second divorce is effective. As for the first divorce, it is binding unless it is highly probable that she would carry out her threat of suicide; in that case, the divorce does not take effect. As for the third, writing a divorce is an ambiguous expression (kinayah) that takes effect with intention. If he intended to enact the divorce, it takes effect; if he intended it as a threat, it does not. If all three divorces have occurred, the wife becomes unlawful for him and cannot return to him until she marries another husband. If one or two divorces have occurred, he can take her back as long as she is within her iddah (waiting period). If the iddah has ended, she is not lawful for him except with a new contract."