We had a church member attorney come to relief society one time and he gave a presentation on things very similar to this. He told about a young married couple who had just had their first child and were on a road trip and almost home. He hit a bridge rail and it impaled her. The husband was seriously injured in out of it for days. The child was put into foster care and stayed there for a while due to not having anything official drawn up on their newborn infant. They were both unavailable. Mom was dead and dad was in a coma. No family member was allowed to take the child because they didn't know the parents wishes.
He was finally able to get his child home but it took long long months and that child had bonded to the foster family. It was very hard on him but he worked through the visitations and all to help the baby transfer attachment to him.
The attorney suggested you have papers on file regarding all your children. Stating financial boundaries, guardianship, living arrangements, and so forth, in the event of death or being unavailable. Get copies of it to the local hospitals and doctors offices they use. That way all that has to happen is showing an ID.
Another thing he said was that in a will the parent should specify "I want my children to go to "Insert name here" if I am unable to care for them or are deceased. If that person is unable to provide care or chooses not to then I would like for one of the following to take in my children". This list should be updated when someone moves away or dies or changes where you don't want them to have your children.
You can also list reasons you want your children to go to that specific person. You can also list reasons you do NOT want them to go to certain people too.
When I was a nanny the parents were members of our church ward. I had been working for them for a while and they asked me and my husband to come visit with them. They proposed that "if" anything happened to them would we consider taking their children and raising them, would we raise them in the church, they presented us with income budgets, we'd get a stipend to live on for ourselves, their kids care would have about a million each year to live on that would include housing, all personal needs, food, vehicles, health insurance, did I mention food? For 7?, we thought about it and prayed about it and said yes. Thank goodness we never had to even think about it again. They had listed several reasons they didn't want family to take their kids and it was worded nicely but specific.
So, when you ask about what to do about your adult children...I agree, it's a great idea to give someone this authority. If they get off to college and do like so many young ones do, get drunk, try new stuff, act crazy and have fun, they might end up with alcohol poisoning, a drug reaction coma, or more. I think it's smart to have someone you trust with that sort of authority that specifically knows your wishes and wants. It's good for you and for them.
I have an adult friend. She is in her 50s and lives alone. She is disabled but able to do for herself. She has an older cousin that she has designated, and set up in court, to be her spokesperson in the event she is unable to tell anyone her wishes. It specifically states she is not to be taken off life support. That she wants to be buried and not cremated. She wants her things to go here and there and her cousin is to have complete access to any money she has in her banking, savings, or retirement accounts.
This protects both of them. Her cousin may not feel the same way about everything in her own life but she will fight tooth and nail for my friend to have her wishes fulfilled as to her care in the event she can't do it herself.
Having it written down isn't enough. It needs to be a legally binding document so that no one else can come in and show something else and say it's from the same person.