Can I take the power of attorney document for health into the hospital for my mother, the witness and myself to sign?

I was stopped by the hospital doing anything or even being with my mother when she was assessed. They said she has full capacity. They then stopped my mother signing the POA form. I am already for her finances and have been a while. But Mother never said to do the health. She has been diagnosed with dementia, but still has capacity but has for the last number of years had me dealing with her health matters. Not that she ever followed advice given by Doctors or myself. The hospital have said that Mother wants to go into a care home. She has told me she does not want to. I am now feeling that the hospital are trying to control my mother and that putting her into a care home she will deteriate very quickly and no longer a burden on NHS. I have got things set up in place at home for her but they are not listening. What can I do I am getting totally stressed. I mean why can carers not pop round in the day while i am at work and my son is at college.