What rights does a POA have while their agent is in a nursing home?

I am durable and Healthcare power of attorney of my mom and have lived with her for the past 2 years and have been taking care of her . She is 91 and has been diagnosed with Alzheimer's. About 2 months ago she fell and broke her hip. I thought it would be best to put her in a facility that is, I don't know if it's a nursing home or skilled facility but it also is a rehabilitation facility. I was hoping she could go there and get stronger and then bring her back home but the physical therapist didn't think she was making any progress so now she isn't getting any physical therapy. I was just wondering what my rights are as her durable and Healthcare POA as far as being in charge of her care in there or bringing her home for visits or maybe permanently if I can handle it. (My health has taken a turn for the worst). I was wondering do I have to give them a notice in there? They kind of sort of treat me like I have no rights so I was just curious and they never include me or keep me involved in her care. Also... I had to apply for Medicaid for her because all she has is Medicare and I know she will meet the qualifications like in income and assets if she stays in the nursing facility but I don't think she will if I bring her home and if I bring her back home I need to get some help with her because it was hard enough before she found broke her hip and now with them not working with her in there she is really really weak. And another thing I might mention is my half brother who's 15 years older that I barely know, when he found out that she switched power of attorney he used to be and then she switched it to me he was so worried about the money in the bank that he tricked her into going and withdrawing all her money and then he put it all in his name as has never brought her a penny in the last 3 years. He was also mad because originally, he was given unrestricted power of attorney and it said that he could do anything he wanted to with this house but it was in the will that I was supposed get it, so he powdered about that and then he took over a paper for my mom to sign she signed it she don't know what it was and I guess he told her that he was a boss he was in charge now so my thinking was oh no he's going to take the house and kick her out so we went and put it in my name now upon meeting with the nursing home financials person he is telling me that they will do a 5-year look back and they may not approve her Medicaid for 8 or 9 months so I don't know what I'm going to do. I fell around Christmas Eve and hit my head and now have brain damage and I don't know what I am doing and I don't know where to turn for help. I also don't have any income right now so I can't afford an attorney. I just want to do what's best for my mom and also the financial guy at the nursing home also had me sign a paper it is a estate recovery paper that says when my mom passes away that they will take this house to pay back the state and I said that's fine because I need to make sure my mom is taking care of so any advice you could give on any of these subjects I would really appreciate it