Is a wife suffering from depression permitted to refuse travel for her husband, given the presence of another wife and difficult living conditions, and what is the ruling of Islamic law regarding her refusal of divorce due to the distress she is experiencing, which hinders her recovery and normal life?

It is recommended to be patient and to turn to Allah, for He is the dispeller of harm. There are appropriate supplications for this. The husband and in-laws must maintain good relations. If the husband and his mother behave poorly, they should be advised kindly and reminded of Allah. The husband must be just among his wives, and there is no harm in agreeing to a rotation for him to visit them. If the wife refuses to live with her husband without a valid excuse, she is considered disobedient (nashiz), and her right to equal division (of time/support) is forfeited. If the wife requests a divorce due to harm, it is desirable for the husband to grant her request. If he does not, she should refer her case to a Sharia judge, while noting that divorce is not always in one's best interest.