Is it permissible to give the brother's wife a monthly sum from his deposited money without his knowledge, with the aim of resolving the dispute between the spouses due to insufficient maintenance, and is this considered an allowance (rukhṣah) granted by the Prophet (peace be upon him) to Hind bint ‘Utbah, or is it an act of disposing of a trust without the owner's knowledge?

If the brother falls short in providing for his wife, he is sinful, and it is obligatory upon you to command him to spend on her according to what is customary. If he does not do so, she may take from his money what suffices her according to what is customary, if she is able. Otherwise, she may refer the matter to the judiciary. If all of that is not possible, then it is permissible for you to give her what she needs for her sustenance without your brother's knowledge, and some scholars have gone so far as to say that this is obligatory.