Is mixing a father's money with the money of his mentally handicapped sister—for whom he is a guardian and who has a sufficient pension—for household expenses considered a violation of Allah's saying: "And do not consume their property (by mixing it) with your own"? And if mixing is impermissible, how should the father calculate the costs of his sister's stay in the family's owned home? And does the verse "and do not exchange the bad for the good" apply to the mentally handicapped who cannot discern between good and bad?

Your father must manage his mentally disabled sister's money in a way that serves her best interest. He can spend on her from it and take a reasonable عوض (compensation) for her living in his house, because he is not obligated to financially support her if she has sufficient funds. However, if he voluntarily houses her without charge, that is better. It is permissible for him to mix her money, which is spent on her needs, with his own money and that of his dependents, based on the verse: "And if you mix with them, then they are your brethren." This does not fall under the prohibition of devouring the property of orphans. The verse: "And do not exchange the bad for the good" includes the mentally disabled and warns against betraying trusts.