I think you need to look to your Okla State statutes for sure. If you think about it this far fetched way, I think you will decide it just doesn't pass a "smell" test:
I have a trust drafted, place my assets in it and appoint you to trustee to look after my best interests. Let's say I have a child that I don't trust. I believe that given an opportunity, this child will abscond with my assets and withhold life support, just to get at my money. But I trust you explicitly. Now let's say that time passes and you decide to take a six-month sabbatical but you are afraid to tell me for fear that I will try to talk you out of it - after all who will look after me. Since you are friends with my child, and you don't really know why I chose you over him/her to be my trustee, you give my child your POA, thinking that they will look after me temporarily while you are gone. You go away and while you are gone, my child gains access to my assets, spends them, sells my house, moves me to the most disgusting, dark, cheap, and faraway nursing home s/he can find.
......No, I don't think that the POA that you give to somebody to act as your attorney-in-fact carries through to giving that POA the ability to act on my behalf. Silly scenario - I know, but I think you get the picture