Praise be to Allah.
We ask Allaah the Almighty to make us and you steadfast in adhering to His religion, and to bless us and you with more obedience and righteousness.
With regard to what you are asking about, it is better for you to stay with this girl towards whom your heart is inclined, and who feels likewise about you, and who has no faults that would cause you to leave her. All that there is, is that she needs a little care and encouragement and sound Islamic education to accept and follow the commands of Allaah.
A lot of that may come after marriage, especially if you treat her nicely and move her into a better environment than the one she is in, which is what we advise and encourage you to do.
There is no reason why a woman who loves her religion and is obedient to her husband should not respond to the command of Allaah as regards her clothing, especially since this will make her husband love and respect her more.
Her refusal to wear niqaab may be because of the lies fabricated by some of those who are ignorant and who follow their own whims and desires, who say that the niqaab is a custom inherited from the Jaahiliyyah and that it was not brought by Islam. You should explain to her the ruling on a woman covering her face, with evidence from the Qur’aan and Sunnah, and tell her that the scholars are unanimously agreed that this ruling is prescribed in Islam.
Remind her of the Sahaabi women who hastened to tear their aprons so that they could cover their faces after the verse of hijab was revealed, and encourage her to have righteous friends. Tell her that this world is transient and soon each of us will meet our Lord with our deeds.
Neither you nor she should worry about what your families will say. As for such environments where the rulings of Islam are not known and people cannot differentiate between proper adherence to Islam and extremism no attention should be paid to them or to what they say about one who adheres to the path of righteousness.
If your wife does not respond to the Islamic injunction to cover the face, then be patient with her, and try to convey the message to her in some other way, such as from another women who is involved in da’wah, or by means of tapes and books by scholars whose knowledge and religious commitment can be trusted.
Seek the help of Allaah and persist in calling upon Him, asking Him for support and help to establish a household based on what our Lord loves and is pleased with.
Show her the answer to question no. 21134, which speaks of the obligation to wear niqaab according to the Qur’aan and Sunnah.
And please see question no. 20343 which speaks of the husband’s duty to advise his wife and how he may do so.
And Allaah is the Source of strength.