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.
First of all, you should know dear brother that a mother has a great right on her children. When the Prophet was asked: "Whom among the people deserves my best companionship?, he replied: "Your mother", and he repeated this thrice." [Al-Bukhari].
When the mother reaches old age, the right of taking care of her becomes greater, and being kind to her becomes even more confirmed. Allaah Says (what means): {If one of them or both of them attain old age in your life, say not to them a word of disrespect, nor shout at them but address them in terms of honour. And lower unto them the wing of submission and humility through mercy, and say: "My Lord! Bestow on them Your Mercy as they did bring me up when I was small."} [Quran 17:23-24].
Therefore, we advise you to fear Allaah and not be negligent about your duties towards your mother, and you should not favor your wife over her.
We also advise you to remind your wife of Allaah and that she should be steadfast on His Religion, and remind her about your duties towards your mother. You may use beneficial books and Islamic tapes to achieve this objective. If she becomes righteous, all perfect praise be to Allaah, otherwise, if she refuses to perform her religious requirements and is rude to your mother, then there is no good in keeping a wife who is not religions, who does not have a good moral conduct and who is barren. Rather, it is senseless to keep such a wife.
For more benefit on how to deal with a disobedient wife, please refer to Fataawa 85402 and 89480, and Fataawa 82254 and 84942 on the rights of parents.
Also, it should be noted that denying the obligation of performing Hajj and the obligation of performing the Friday prayer is an act of apostasy which takes a person out of the fold of Islam. Therefore, whoever denies the obligation of Hajj and that of the Friday prayer becomes a non-Muslim even if he was a Muslim beforehand, and becomes an apostate, which in turn, invalidates the marriage contract; for more benefit in this regard, please refer to Fatwa 88845 and 90497.
Finally, for more benefit on a wife who does not perform the prayer and who does not wear Hijab, please refer to Fatwa 83244.
Allaah Knows best.