At request of the department on aging I obtained POA of mother with early dementia. Do I have a right to stop siblings from contacting her?

My sister had been assisting her but started getting verbally and emotionally abusive to her, she was turned in to area on aging several times and mom was scared of her so she wouldn’t tell them anything. Since then mom has fallen and obtained a head injury. I went to PA and brought my mom back to Colorado to care for her. The doctor asked her other children who would step up to take her and none of them did, there are 7 other children. I also asked two of my other sisters to be on the POA with me. The lawyer made sure mom was agreeable with it and understood it at the time. Since bringing mom here to Colorado, my siblings have become hateful and upset mom all the time. Mom suffers from anxiety and was just diagnosed with Alzhiemer's. Do I have a right to stop them from contacting her? Now I have never wanted this but it is causing her more anguish. I have actually sent her home twice in the last year. I promised her as long as she could travel I would make sure she would continue going home. Now they are threatening to take me to court and take her back there. Can they do that, since I have POA? The two sisters with POA aren’t involved with wanting to come get her. Mom has said she is better mentally when she doesn’t talk to them. I want what is best for mom and I know she is homesick but I know she won’t get the care she deserves because they didn’t care for her when she lived back there. Hardly ever went to see her or called her. I am done with this harming mom