I married an American woman; I tried to convert her to Islam and made her to accept Islam. But she always refused to follow Islam. Now I feel that no more I can live with her. She always drinks at home and she keeps a dog with her. Right now I can't leave her for official reasons. I want to ask does Allah accept my prayers and forgive me?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is permissible for a Muslim to get married to a woman of the People of the Book if the conditions of a Muslim marriage are met, and if this woman is chaste.

As regard the relationship of the husband with her, he should not prevent her from practising her religion.

However, he has to forbid her from doing things that are permissible in her religion like the drinking of alcohol, etc. and she has to obey him if that does not harm her.

If that is the case, the brother asking this question, has the right to forbid his wife to drink alcohol, and forbid her to keep the dog and she has to obey him in that as it not part of her acts of worship which the husband should respect.

If she does not obey him, she is disobedient.  So he has to follow the steps that the Qur'an has mentioned in relation to women in her case.  First, he has to remind her about her duty towards her husband and her obedience to him. Then if she still remains the same, he has to sleep separately from her.  If again she is not deterred, he can slightly hit her if she will not be harmed by that.  And if she persists, then it would be better to divorce her even if he is going to lose some benefits of this worldly life, unless he fears that his children will be taken away from him, and left with their mother and fears that she will destroy their religion, so in this case he has to be patient with her and treat her nicely hoping that Allah will make him a means for her guidance.

On the other hand, we would like to draw the attention of the brother asking the question, that what has been mentioned about his wife does not affect the validity of his Salat if it is performed properly.

Allah knows best.