If it were my parents or anyone that I loved that needed care: I would offer to pay for groceries, their electric bill (directly) or any other kind of bills that I could pay directly. I would not hand money over to siblings or anyone for that matter, that had already mismanaged funds.
Perhaps by saying “I am happy to help dad, I will mail a check for $50 monthly to dad’s electric company and $50 monthly to dad’s insurance please give me the billing information” or whatever the amount that the sibling can afford. Even if the books were to be opened there is no way to guarantee that the siblings with power are not going to mismanage things again. It sounds as if they gave loans to personal business friends? What is to keep them from doing that again? Now they want siblings to hand over cash with no questions asked?
The siblings that mismanaged things should be apologetic, gracious, upfront about what happened and transparent. However from what you wrote it seems they are showing resistance to opening up the books. Perhaps the only way around this is for the other siblings to offer to pay dad’s bills directly. If the siblings in charge refuse this offer then there is reason to be suspicious because then they only want cash, not help for dad.
What a shame, this is so sad.