Is it permissible for a mother to buy food for her children without the knowledge of the wealthy father who deprives them of some beneficial and inexpensive foods, and is it permissible for the children to eat from it?

Obeying one's father is obligatory in matters that serve a valid purpose, such as fearing harm. However, if he commands something foolish, obedience is not obligatory. If the mother purchases from the father's money without his knowledge, this is not permissible unless he withholds the obligatory expenditure, in which case she may take what is sufficient for her needs in a reasonable manner.