What is the ruling regarding a wife swearing falsely upon the Qur'an concerning money she took from her husband's house without his knowledge, and is she sinful for that, and what is the expiation due upon her, knowing that she did so to reclaim part of her right due to her husband's failure to spend on her and their children?

If a husband expels his wife and children, abandons their financial support, and wrongfully seizes their belongings, he is unjust and transgresses the bounds of Allah. However, this does not justify swearing a false oath to obtain rights. He could have been compelled to return the money or provide for the children, or they could have resorted to the judiciary to force him to do so. What is obligatory is repentance from the false oath, and it is more prudent to offer expiation for a false oath.