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 your brother in-law is as you stated, that his behaviour is bad and he has established a forbidden relationship with a marriageable woman who is a Christian, and that his living with you could cause an affliction between you and your husband, then he does not deserve to live with you in the same house. In addition to this, if you are sharing the amenities in the house to an extent that he can see you whenever he wants, then the matter is more serious. The Prophet said: "Beware of entering upon marriageable women." A man from the Ansaar remarked: "O! Messenger of Allaah, what about an in-law? He replied: He is death itself (i.e. his seclusion with women is as serious and dangerous as death)." [Al-Bukhari and Muslim] Furthermore, on one hand, the jurists stated that the wife has the right for a separate accommodation. On the other hand, the wife has the right to give birth to children, so it is not permissible for her husband to prevent her from this right without a sound religious reason. It is not permissible for him to give an excuse that he is not able to provide for the children, because it is Allaah who provides for His Servants. The provision and age of every new-born is predestined. So how can one accept the claim of your husband that he is not able to provide for a new-born while he is providing for his brother in the manner that you mentioned?
Anyway, you should advise your husband according to what we have mentioned while being wise and using good words and being keen on what benefits you. If the intention is good, then Allaah will enable you to rectify the matters between you two. Allaah says (which means): {If they both desire reconciliation, Allaah will cause it between them. Indeed Allaah is Ever All-Knower, Well-Acquainted with all things.}[Quran 4:35]. Do not forget to implore Allaah to enable your husband to accept what is more correct and righteous.
Finally, the following two matters should be noted:
1) It is forbidden for your husband to let his brother to come to your home with this woman.
2) One should endeavour to advise your brother in-law with soft words and remind him of Allaah. It might be that Allaah will turn him into a righteous man.
Allaah knows best.