Is it permissible to take money from the father without his knowledge to buy medicine and fruit for the mother, given that the father is aware of his financial capability and his refusal to provide them, and the children's material need for it?

The default rule is that it is not permissible to take anything from the father's or husband's money without his permission.

However, a wife is permitted to take from her husband's money without his knowledge, an amount sufficient for her maintenance according to what is customary, if he is remiss in providing for her. The same applies to a daughter who has no earnings or money, if her father does not provide for her according to what is customary.

The proof for this is the Prophet's (peace and blessings be upon him) statement to Hind: "Take what is sufficient for you and your child according to what is customary."

Among the obligatory expenses for a father is the cost of medicine for his child, within customary limits.