If there are aunts and uncles, presumably some of them are siblings of your father-in-law, as closely related as his children...
A technicality: Not sure in the USA, but over here that's not correct. Relation is measured in grades being those the basic parent-child "distance". So you're related in the first grade to your parents or children, but in the second grade to your siblings (1 grade distance from you to your parents, another one from your parents to them) so, unless the father in law has a living parent, no one is more closely related to him than his children.
So for lack of a better way of understanding, I would just ask a lawyer.
This is a very tough situation and I don't think it was any lack of skill on your part that made you unable to get through to your brother-in-law this time. I don't think the world's champion hostage negotiator could have done it on the first try.
I'm a little unclear on one aspect, though. You say your goal is to get your brother-in-law to allow your wife to talk to medical staff. But the family not your wife is asking you to talk to him? Yet they're not asking for anyone else, other than your wife, to be able to talk to medical staff? If there are aunts and uncles, presumably some of them are siblings of your father-in-law, as closely related as his children and with as much right to be involved in medical discussions as your wife has. Yet they're not trying to get themselves involved in the process? Only your wife?
(Also, as I commented elsewhere in the thread, if I were in your position, I would not want to take this on unless I was sure my wife was OK with it. I can totally see that she might just not want to have the discussion herself because of her history with her brother; I just would want to be sure that she was OK with what was being done.)