If I have a durable power of attorney over the financial assets of my mother, what is the best way to handle if another person is refusing to give mom's funds over?

I hate to say it, but your only recourse could be to say that they have so much time to return the money or you will see and elder law attorney. That could do the trick. You know, of course, this will cause more family strain, but it sounds as if this relationship is already strained. If it's a lot of money, it may be worth legal action. If it's not very much (and this is different for everyone), then you may have to just let it go. In the end, it's how hard do you want to fight?
Good luck,
Carol