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.
If the case is as you mentioned that the in-laws of your paternal cousin beat and harm her, this is a grave form of injustice. They must be advised to fear Allaah and repent to Him of that. They must repent as well of neglecting the teachings of their religion, especially regarding their drinking alcohol and not performing the prayers regularly which is the main pillar of Islam. In fact, Quran sets a severe warning against neglecting the prayers. Allaah The Almighty Says (what means): {But there came after them successors who neglected prayer and pursued desires; so they are going to meet evil.}[Quran 19:59]
As for this woman's work, in principle, she is not allowed to go out to work except with her husband's permission as long as he provides for her. But if he does not provide for her, he will not be permitted to prevent her from going out to work because – according to Muslim jurists – he has not fulfilled his duties, so he has no right to prevent her.
We do not know the nature of the demands that her parents did not fulfill. However, supposing that her parents did not fulfill these demands, she is not required to ask them to fulfill them. So, how could she be beaten because she did not ask her parents to fulfill these demands? Also, she is not required to serve the family of her husband, and it is shameful that the husband tells her that he married her for that purpose only. For further information, see Fatwa 84909.
Moreover, this husband is obliged to provide his wife with a separate accommodation, and it is not permissible for him to force her to live with his family unless it is a separate part of the house with its own facilities. For further information, see Fatwa 84608. Furthermore, this wife is not required to accept the conditions that her husband mentioned, nor should he threaten her with marrying another woman if she did not accept his conditions. If he married another woman, it would be obligatory upon him to treat them equally, since justice is the condition of marrying more than one wife. Allaah The Almighty Says (what means): {But if you fear that you will not be just, then [marry only] one.}[Quran 4:3]
Finally, if this man is having illicit relationships with other women and does not support his wife financially, it will be preferable for her to ask for a divorce from him, particularly because his family members harm her and he insists that she should remain with them and serve them and Allaah may grant her a better husband.