All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If the matter is as you mentioned in the question that it is your husband who caused the divorce of that woman from her husband, then he has committed a great sin. For more benefit on spoiling the relationship between a wife and her husband, please refer to Fatwa 92056.
If that woman asked her husband to divorce her without any sound reason, then she is sinful as it is forbidden to do so. For more benefit in this regard, please refer to Fataawa 90676 and 84309. Therefore, it is an obligation to advise both of them to repent to Allaah.
As regards polygyny, then it is religiously permissible for a man to marry more than one wife provided he is able to fulfil the condition of doing so, which is to be just between them. Indeed, there are many religious benefits in polygamy; for more benefit, please refer to Fataawa 90132 and 89883.
Therefore, if your husband is able to be just between his wives, then you are not permitted to disapprove, as this may imply denying something which Allaah has permitted for men (one of whom is your husband). Allaah Says (what means): {It is not for a believing man or a believing woman, when Allaah and His Messenger have decided a matter, that they should [thereafter] have any choice about their affair. And whoever disobeys Allaah and His Messenger has certainly strayed into clear error.}[Quran 33:36]. However, according to the view of some scholars (which is the predominant opinion) if your husband agreed before the marriage contract took place to the condition of not marrying another woman as long as you are his wife, then he is obliged to fulfil this condition.
Finally, the following matters should be mentioned:
1- The scholars differed in opinion about the ruling on whoever marries a woman whom he caused the spoiling of the relationship between her and her husband. Some of them are of the view that such marriage is void. However, some other scholars are of the view that such marriage is valid while the husband is sinful, and this is the correct opinion, Allaah willing, because if the marriage fulfils its conditions, then it is valid and the spoiling of relationship between the wife and her husband does not render the marriage contract void.
2- It is not permissible for a husband to mistreat his wife by insulting her, beating her and the like, unless this is due to a sound reason and provided that it is done according to the permissible way of hitting the wife, as in the case when the wife is disobedient please refer to Fatwa 89480.
3- A woman is marriageable in regard to a man unless he conducts the marriage contract with her. Therefore, it is not permissible for him to establish an affectionate relationship with her, and he is obliged to repent and stop such a relationship if any, even if he does not make an oath about it. Then, if he makes an oath to stop such a relationship and breaks his promise, then he is obliged to expiate for breaking his oath.
Allaah Knows best.