Would the nursing home discharge my dad against my consent?

My parents are in their 80s and have been living with for over 18 years. The past 5 years have been very difficult b/c my parents stopped talking to each other after my dad accused my mom of infidelity from 40+ years ago(!). Let alone the event never took place. My dad also managed to alienate my husband by accusing accusing us of turning off his electricity (he tripped the circuit by turning on all the appliances in his room at the same time) and stealing his money (he lived with us for over 18 years without contributing a penny toward his living expenses). No one at home would come near my dad or talk to him so I'm the only one at home to help him and he needs constant help from getting his meals, turning up the volume on his iPad to finding misplaced remote controls. My dad picks fights with everyone even his helper who comes to the house 4 hours per day. Nothing is ever good enough for him. He even told me that he has not been happier living with us for the past 18 years. Sometimes I wanted to start a blog about all the crazy stuff that my dad does and says that my friends couldn't believe actually happened. I found a lot of support from talking to people about my situation and through reading the posts in the Caregiver Forum.

Fast forward to today. We managed to get him placed in a long term nursing home after going through rehab for a fall. He has been calling us every week wanting us to come bring him home. I have decided that my dad will not be happy wherever he resides so it is better to have one person miserable (him staying at the nursing home) than to have my entire family miserable if I bring my dad home.

Last week he asked me to tell the nursing home that his insurance won't pay for his stay so they will send him home. I told him that the nursing home deals with the insurance company directly and they would not believe what I tell them. Both my brother and I have explained to him that he can't come home because there are no one at home to provide the care that he gets at the nursing home. Let night the nursing home called me saying that he asked the nurses to pack up his bag so he can go home. The nurses said they do not have a discharge order so he is not going anywhere.

My question is If he keeps on throwing a fuss at the nursing home, would they get tired of him and discharge him? If they notify me that they are discharging him, do I have to pick him up? Thanks for listening to me and appreciate any advices you can give me.