This is a test from Allah. Allah has tested some Prophets through their wives. Your responsibility is to exert all efforts possible to remind your wife of Allah and to strengthen her faith. This may happen by asking Allah in your prayers to guide her to the straight path and by consistently advising her. She might have been exposed to some circumstances or bad experience which affected her commitment and dedication. She might have been raised in a corrupt environment.

 

In case you both have children, they may be greatly affected by your separation. This is the reason you have to take all possible means for getting her closer to Allah expecting reward from Him. My advice is to be patient to her, but if you have strong feeling she will affect your religion you may, then, divorce her.