Is the legitimacy of a husband's going out for days with Jama'at al-Tabligh, leaving his wife and children in a non-Muslim country—is this from the Sunnah, or does it conflict with his responsibilities towards his family? And should the wife trust his statement, "I entrust you to Allah," under these circumstances?

The people most entitled to a man's care and protection are his family and household. He must balance his obligations and prioritize what is most important. A man's care for his family includes providing for them and protecting them from danger. This varies according to time and place. If the place is safe, he may travel; otherwise, he must remain with them or ensure their care. The husband's argument citing the story of Ibrahim (peace be upon him) is incorrect, because Ibrahim's action was by Allah's command and divine wisdom, whereas there is no command for a man to neglect his family. It is advisable for the spouses to reach a calm understanding and for each to consider the needs and circumstances of the other.