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.
Understanding and mutual respect should prevail in the Muslim family between the husband and wife. In such circumstances [i.e. the situation mentioned in the question], the husband should take into consideration his wife's feelings especially after the loss of her brother in addition to the difficulties of pregnancy. On the contrary, the wife should not be neglect the due rights of her husband because of what happened, especially that in Islam a woman is forbidden to mourn anyone other than her husband for more than three days. The Prophet said: "It is not permissible for a woman who believes in Allaah and the Last Day to mourn a dead person more than three days, except her husband whom she should mourn for a period of four months and ten days." [Al-Bukhari and Muslim] Besides, a husband should not be absent from his wife as a means of disciplining her, nor should his marriage to a second wife be a means of doing so. Such behaviour could worsen the dispute and perturb the life in the family.
As regards a man marrying a second wife, this is something permissible as long as he is able to be just between them. It is not a condition for him to inform his first wife about it or to seek her consent in this regard. The first wife should fear Allaah and be patient. It could be that there is good for her in this marriage [in her husband marrying a second wife].
With regard to the husband being absent from his wife, if this is for a period of six months or more, then this is not permissible without her consent, but if it is for a period of less than six months, then there is no harm in it. However, if the husband is neglectful about her due rights like spending on her and the like, then he is sinful.
However, it is not permissible for the mother of the husband to order him to neglect his wife and it is not permissible for him to obey her in this. The Prophet said: "It is enough a sin for a man to neglect those on whom he is obliged to spend." [Al-Bukhari and Muslim]
Concerning this man establishing an affectionate relationship with a marriageable woman, this is forbidden, and he is sinful if he had done so. It is an obligation, therefore, to advise him to repent to Allaah. As regards the relationship of your brother in-law with his fiancée, please refer to Fataawa 81940 and 86143.
Allaah Knows best.