Is it permissible for the wife to keep what remains of the money allocated by the husband for the children's food without his knowledge, and is it permissible to take a portion of this money?

The principle is that the wife is entrusted with her husband's money and acts as his agent concerning the children's maintenance. It is not permissible for her to take anything from it for herself except with his explicit or customary permission. Customary permission applies when it is customary for him to be pleased with it and his consent is known. However, if there is doubt about his consent or if he is stingy, she may not take anything except with his explicit permission. If you know that the woman took the money with customary permission, then there is no blame upon you. Otherwise, you must return it and forbid her from doing that.