I've seen this before, but really, there is ABSOLUTELY NO REASON for a brother to make someone designate him as their "health care agent" when there is family available.
I would visit an attorney, have the appropriate documents drawn up (it's not that expensive) and distributed among relatives, doctors, etc. as appropriate (unless they are JWs, of course) and tear up the other stuff.
Should an emergency happen and they show up at the hospital waiving papers around ask the nursing staff to call security.
If an emergency never happens, they'll never know.
BUT-it is OUTRAGEOUS that they would ask to be her "representative".