My sister wants to send my mother to a nursing home. please help.

Hello. My mom was hospitalized on Feb. 17th of 2014 for one week. She is 52 years old, and turns out she has been having a series of strokes for years and never knew. After she left the hospital she came and lived with me and my family. My sister was upset with that. Since Feb I have taken my mom to every single doctors and specialist appointment. I have also applied for her to get medicaid (which she was approved), ssi (which she was approved), and disability (just recently approved). However, the only way disability would give her benefits was if she had a representative payee, because she was approved based on mental status. I am her payee. Now that my sister knows this, she is adamant in putting my mother into a home. She also wants to get power of attorney over my mother. My sister is very money hungry and I am scared. My mom is more than welcome to live with me and my family, and she wants to! She doesn't want to go to a home. Please help me. I believe I need to take some action.