My question involves a power of attorney in the state of: Michigan

My grandmother lives alone and has been showing signs of alzheimers for the last 2 years. Recently she was in ICU because her kidneys shut down on her. My Uncle had been calliing her house and when she didn't pick up he went to check on her. The doctors said he got to her just in time. My mother and Uncles go over frequently to check on her but because of health problems in their own lives they are unable to give her the care she needs. We believe that she needs 24 hour care but she refuses to allow people into her home. She is digressing more and more each day and we are afraid of her doing physical harm to herself. When she was in ICU her doctors confirmed that she was in the beginning stages of alzheimers which runs in our family. She is a very independent woman though and has lived alone for many years. My mother and Uncles agree that she needs help that can only be provided through an elderly home facility but in order to place her in one we need to gain power of attorney, which is something that she will not give. Is there anything we can do?