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, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
Your wife’s brother has no right to threaten to divorce your sister if you took another wife. Allaah has made polygyny lawful to those men who are capable of treating their wives on a footing of equality. Moreover, it is disliked for a man to divorce his wife without a legitimate reason. Some scholars even deemed it forbidden, given the consequent evils that are mostly incurred in such a case. This has been highlighted in Fataawa divorced their wives">104995 and 87786. Hence, your wife’s brother may be held sinful for divorcing your sister for no legitimate reason.
It is worth highlighting that the Islamic ruling on marriage varies according to people’s different situations and needs. If you do not fear falling into Fitnah (temptation/trouble, e.g. approaching a woman unlawful to you or engaging in any other forbidden sexual outlet) if you do not take another wife, marriage is not considered obligatory in this case. Therefore, your obedience to your mother and giving up the idea of a second marriage is considered obligatory. This is so if your marriage may cause her justifiable harm which is not a result of her foolishness and ignorance. Verily, what is obligatory - obeying your mother - should be given precedence over what is not obligatory - marriage in such a case.
However, if you fear falling into Fitnah if you do not take another wife, in this case such a marriage is obligatory. In this case, it is not incumbent on you to obey your mother and give up the idea of the second marriage, because children’s obedience to their parents is only in what is good. Verily, harming oneself is not good. Please, refer to Fatwa 245677 about the criteria and limits of children’s obedience to the parents.
However, if you can adhere to piety and give up the idea of having a second wife so as to show dutifulness towards your mother and preserve your sister’s family, this would be commendable of you. You would be generously rewarded for your dutifulness to your mother and eagerness to gain her pleasure. You should not forget that taking a second wife may incur adverse effects on your family, and this is often the case as we know.
With regard to this woman, we advise you to show kindness to her and take care of her two daughters. This is an area of doing good. Verily, Allaah, The Exalted, does not allow the rewards of the good doers to be lost, especially since Allaah has bestowed favors upon you and granted you abundant wealth. You can also help her find a righteous husband; this is commendable. Allaah, The Exalted, says (what means): {… and do good - that you may succeed.}[Quran 22:77]
Allaah Knows best.