What should a wife do if her husband insists on remaining in a non-Muslim country, which is affecting his faith?

It is not permissible for a Muslim to reside in lands of disbelievers unless there is a necessity, an urgent need, or a legitimate benefit. The Prophet ﷺ forbade this, saying: "I am free from any Muslim who resides among the polytheists."

As for the wife whose husband refuses to reside in Muslim lands: if he is compelled, or has an urgent need, or a legitimate benefit, then she should excuse him and be patient. However, if this is not the case, she should advise him and explain the Islamic ruling to him, seek help from his family and friends, and supplicate much for him. If he does not respond, and she fears for her faith or is harmed, she may refer her case to those who resolve disputes in those lands to remove the harm from her, whether through divorce or other means.