His wife does not accept advice. What is the solution?
Question

I got maried 4 years before. My wife was not having any religious attitude at all. She was strongly against observing hijab/niqab. She didn't even covered her head. On my asking to observe hijab, she simply refused and said that she was a learned girl and that she knows her good or bad. I didn't loose heart and kept on trying to convince her and engrave in her heart the fear and greatness of allah. Now after 4 years, there is a little improvement. She has started a little bit of hijab(i.e., she covers her head and chest) but is still not convinced to do niqaab. She offers her prayer but recites quran wrongly (i.e., her pronunciation is not correct). She is not interested to learn reading quran. She is casual to learn about the problems of her periods and mixes up her days and leaves the prayers one or two days more than her periods. She doesnot accept any body's remarks and considers her own decision as final. What line of action should I adopt as she does not bear any harsh words or behavior.
Praise be to Allah.Undoubtedly your wife is persisting in making a serious mistake, and we ask Allah to guide her. The most serious thing that you mention about her is the matter of her careless attitude towards prayer, because not praying leads – Allah forbid – to one becoming beyond the pale of Islam, because the Prophet (peace and blessings of Allah be upon him) said: “What stands between a man and shirk or kufr is his giving up prayer.” (Narrated by Muslim, 82). This applies to one who does not pray at all. But some of the scholars (may Allah have mercy on them) thought that a person who fails to pray one prayer on time also becomes a kaafir. See al-Mughni, 3/354). This points to the seriousness of the matter. 
You have done your duty towards your wife by guiding and advising her, and this has borne fruit. Even though it may be incomplete, it is still a positive step which indicates that there is goodness in your wife and that she is prepared to change the rest. Yes, that may be slow but it is possible. You see that in the beginning she was not convinced of hijaab and did not wear it at all, but after the noble efforts on your part she has started to wear it partially. Even though it is not full hijaab as it should be worn, it still gives us hope and points to hidden goodness in her. You can bring it to the surface so that she will wear proper hijaab on the basis of conviction and her own desire to do it, as time goes by and as you continue your efforts. This means that you must continue to advise her and not give up, and you will be rewarded for that. The Prophet (peace and blessings of Allah be upon him) said: “If one man were to be guided at your hands, that will be better for you than red camels [i.e., the best kind].” (Narrated by al-Bukhari, no. 6). 
Always remind her of Allah and make her fear Him; tell her of the importance of prayer in Islam and that she has to learn the things that have to do with prayer, such as the rulings on menstruation and post-partum bleeding, because it is obligatory on every woman, when her bleeding stops, to hasten to do ghusl when the time for prayer comes. Try to bring her useful books on that topic, such as the essay by Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) on “The Natural Blood of Women” or some useful tapes. You can help her by sitting and reading with her, or listening to the tapes with her, because this is a kind of cooperating in righteousness and piety. 
[Translator’s note: Shaykh Ibn ‘Uthaymeen’s essay is available in English with additional notes by Bilaal Philips, under the title Islamic Rules on Menstruation and Post-Natal Bleeding, published by Dar al-Fatah, Sharjah, UAE].
With regard to what you mention about her mistakes in reading Quran, if the mistakes are in her recitation of al-Faatihah and are such that they distort or change the meanings of the words – such as reading an’amta [“You [masculine] have bestowed Your grace”] as an’amti [i.e., feminine form of the verb], or any other mistake which would make a listener understand something other than the correct meaning – this means that she has to learn how to read properly, because such mistakes make the prayer invalid, as reciting al-Faatihah is a pillar or essential part of the prayer, without which the prayer is not valid. But if the mistakes do not change the meaning , such as reading “ar-Rahmaan ir-Raheem” as “ar-Rahmaan ur-Raheem”, this does not invalidate the prayer. 
The Muslim must learn to read Quran so that he can recite it correctly, and so that he will not distort the Quran without realizing. 
You have to help her with that, either by teaching her yourself, or by showing her things that will help her, such as tapes of the Quran by readers who are known to recite well. You must also explain to her the virtues of reading Quran and the reward for that. 
So in conclusion you have to continue teaching and advising her, and be patient in doing so. Do not say that she has only responded a little after so much time and effort, for even this little is blessed by Allah. We have a good example in the Prophets, for Nooh called his people for nine hundred and fifty years. Allah says (interpretation of the meaning): 
“And indeed We sent Nooh (Noah) to his people, and he stayed among them a thousand years less fifty years [inviting them to believe in the Oneness of Allah (Monotheism), and discard the false gods and other deities]” [al-‘Ankaboot 29:14]
Yet despite that only a few of his people believed in him. 
Make her enjoy learning about her religion by making it easy for her. Encourage her if you see that she is responding to you, even if it is something small. Know that you are an example for her, so watch what you do and say. Beware of telling her to do something then being the first one to go against that, or of telling her not to do something then being the first one to do it, for this will stop her from accepting your advice, or will delay her. 
You have to be gentle in the way you advise her, for the Prophet (peace and blessings of Allah be upon him) said: “Allah is Kind and loves kindness, and He confers upon kindness that which He does not confer upon severity and does not confer upon anything else besides it (kindness).” (Narrated by Muslim, 2593). 
You must also make a lot of du’aa’ and beseech Allah to open her heart to obedience towards Him and make His religion and laws beloved to her. I ask Allah to help you to do good.