What options do I have with my mother who has dementia and lives with me but I am not her guardian or power of attorney?

My mother lives with me. She is getting worse by the day with dementia. I do not have power of attorney, control of her finances or healthcare proxy. My sister, who has all the power, is ignoring my mother’s deteriorating health. I feel my mother needs to go into assisted living. Do I have the right to put her in one? She has assets to cover this expense. I am afraid she may inadvertently injure herself or even cause a fire where my family would be in danger. I feel my hands are tied and time is of the essence.