A wife exiting her house without her husband's permission
1- What is the stance of the Shari'ah on a wife leaving the marital house without her husband's permission?
2- What is the stance of the Shari'ah on a woman traveling for more than three nights without being accompanied by a mahram [En. A member of her unmarriageable kin]?
1- The Shria'ah has made corresponding rights and duties for both spouses, and while it has made it obligatory upon the wife to remain in the marital house, it has made it obligatory upon the husband to support her within the limits his finances allow. If she has received her advanced marriage payment, she is then commanded [by Allah] to remain in the marital house and not leave without her husband's permission except in the circumstances wherein a wife is permitted to go out such as visiting her parents once every week.
If the wife leaves the marital house and then refuses to return without having an excuse, she is then considered recalcitrant and is not entitled to financial support as of that date.
2- The basic rule when a woman travels is that she be accompanied by a mahram as attested to by the hadith narrated by Ibn 'Abbas (may Allah be pleased with them both) who said: "A woman must not travel unless she is accompanied by a mahram, and no man is to enter into her company unless when she is accompanied by a mahram" [Muslim and Bukhari].
However, some jurists permit a woman to travel alone if the way and destination are safe. They base their opinion on the hadith narrated by 'Adi Ibn Hatem (may Allah be pleased with him) who said that the Prophet told him: "If you live a long life, you will surely see a woman traveling from Hira till she circumambulates the Ka'bah — fearing no one except Allah" [Bukhari].
Imam Ahmad's version of the hadith includes: "I swear by He in whose hands is my soul: verily Allah will bring this matter [the religion of Islam] into completion till a woman travels from Hira and circumambulates the Ka'bah without being accompanied by anyone".
The reason they give for the cause of the prohibition in the first hadith is when the journey is not safe and there is a lack of security. One can follow this opinion because of its facilitation and convenience. However, this is restricted by the husband's approval (if she is married), or her guardian's (if she is not).
Allah Almighty knows best.