Dad lives with my sister, mom lives alone and they both require care. Mom wan'ts to move dad to a nursing home without our consent. Can she do this legally?

My dad has lived with my sister for 5 yrs now. He has alzheimers, had stroke in nov 2009. he is getting home care and is bed ridden now. My mother has had her own place for 10 yrs now. they were never legally seperated. my mother continues to argue with all our family members. its gets worse and worse everyday now. I have 7 siblings. we have been taking care of my dad. my mother can not take care of my dad herself as she has diabetes and bad neuropathy. she has walker and does not have strength to lift my dad. Can my mother legally move my father from his home to either her home or a nursing home without our consent?