What is the ruling regarding a committed wife remaining with a husband and family who do not pray and are not religious, knowing that she is persecuted because of her commitment?

Obedience to Allah must take precedence over obedience to a husband or family in matters that contravene Islamic law. There is no obedience to a creature in disobedience to the Creator. Rather, one must strive to reform the husband and explain the danger of his abandoning prayer, and advise his family in the best manner. If the husband does not respond and maintain his prayers, then divorce should be sought from him. There is no need to fear as long as you remain steadfast in obedience to Allah, for He will never forsake you.