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.
First of all, we shall start with what you mentioned in regard to your wife's beliefs and actions; so you must advise her about this and teach her the matters of her religion and urge her to obey Allaah and obey His Prophet .
If she rectifies herself, especially with regard to her beliefs, then praise be to Allaah, but if she persists in the wrong path, then you may be patient with her as long as her beliefs do not take her out of the fold of Islam, otherwise it becomes an obligation on you to separate from her [i.e. to divorce her].
With regard to the wife not listening to her husband and not obeying him within what is permissible, then this is Nushooz (recalcitrance) on her part. The Quran clarified the treatment of the Nushooz of the wife and the steps that a husband should follow with his recalcitrant wife; this is indeed clarified in Fatwa 85402.
Also, for more benefit on the limits of the obedience of the wife to her husband, please refer to Fatwa 133365.
As regards the wife serving her husband, then there is a difference of opinion amongst the scholars about it; the most preponderant opinion is that she has to serve him within the bounds of what is customary among people (like her and her husband). For more benefit, please refer to Fatwa 86344.
However, among the things that will help treat the wife in this respect, is that her husband should help her as much as possible in household works as this leads to more affection and love between the spouses; for more benefit, please refer to Fatwa 88319.
Hence, both spouses should know and fulfill the rights of each other because this leads to the stability of their family and increases love between them. For more benefit on the rights of the spouses towards each other, please refer to Fatwa 85308 and 85167.
Therefore, you should continue advising your wife, guiding her and reminding her of her obligations towards Allaah and towards her husband, and you should not despair of her being guided as the hearts are in the hands of Allaah and He turns them the way He wishes.
Also, you may make use of beneficial books and tapes in this regard and you may seek the help of any pious woman among the wives of your brothers so that she would admonish her and guide her, and you should be patient as the result of patience is always good.
Allaah Knows best.