Should I insist that my father put me in as the POA since I live with him and I am the primary caretaker?

I ask this question with great need of direction. I moved in with both my elderly parents after my divorce. My mother was diagnosed with COPD and I became her primary caregiver as well as my father's confidant. I work full time and worked around my mother's needs. After her death, my father had a stroke. I retired my position from work to help him recover in the safety of his home. Both my sisters only participated in the decisions of care when hospitalizations were required. They both insisted that dad go to an assisted living so that they could continue his therapy and care. After a month in the hospital, dad wanted to come home. I let my sister's know of his wants and they rejected stating that he needed the care and he has the money. I felt it was my job to do what dad wanted. I took him home and my sisters would not help because of it. They also blamed me when dad was not advancing like he should. He soon fell and broke his bones and again was hospitalized then followed up with rehabilitation center for 1 month. When it was time for out of pocket expense, dad wanted to come home. At that time, I found full time work and needed other committed people to help dad achieve this goal. My sisters again wanted him in a facility telling him that they did not need his money and that he was to spend his savings. I had my support and a care plan in progress. We built him a ramp and took him home. He needed 24 hour care. I planned on staying home, but requested to be paid. My sisters objected to this request wanting again assistant living. Dad said no. He was willing to pay me. My sisters feel that I am not involving them when it comes to big decisions. Through out the years, I had little contact with them and they only invited my parents to family events. Now I am called the employee and that I should have a list of my duties and what I am not to do. The POA is my little sister, and through our dad's care (and some of mom's when she was alive) does not agree with my plan. So, I am afraid that if dad does not change the POA to my authority then he has a high chance of beong placed in a home. When this was shared with my sister, she started yelling and accusing dad of changing the will. She was crying over an hour and dad finally told her he will not change the will. Even though she does not offer financial help, emotional support, nor any care for dad, she feels entitled to being the POA. She does not have dad's best interest in mind, and finds fault with everything I do. I am worried that she will abuse her power, and put her own feelings first. It will be difficult to be the primary caregiver with a toxic sister as the POA. I am constantly working full time and taking care of dad when I am not working. I have become resentful of my sisters and feel that they are always looking for something that I am doing wrong. I do not get compliments or positive reinforcment. I feel I am constantly defending myself with the decisions that dad makes. They both want to be put on the bank accounts to keep track of dad's money. I am not even on them nor have I requested to be. I feel I am not trusted and that they put a bug in dad's ear. Dad has not requested for a change of the will. At this point I am burnt out. The POA has given me disrespect and our relationship has turned toxic. She now spends her energy trying to prove that I am neglecting dads needs or taking advantage of him. I am not worried because there is nothing there. I do not know what to do at this point. Do I stay home to take full-time care of him and demand he changes his POA? Or do I continue to work full-time and go home?