Is it permissible to borrow from money entrusted to me for monthly distribution to the poor of the family, without the permission of the owner of the money, knowing that the amounts reach their beneficiaries without delay?

Trustworthiness is among the virtues enjoined by the Shari'ah. It is forbidden to borrow entrusted property if the borrower is destitute and unable to repay it, or if the entrusted property consists of essentials such as animals and goods. It is disliked to borrow it if it is cash or fungible items, and the trustee has not given permission for its borrowing, unless the owner of the property has explicitly allowed or forbidden it. The most prudent course of action is to seek permission from the owner of the money for whatever you do.