Wow. You all are heroic! My gosh, what a lot of responsibility. I am also at the vomiting stage so I can relate. My father also has cancer and would likely refuse help if we took him home. He does not understand that he is very ill.
At the advice of someone in this group, I contacted ACE (Advocacy Centre for the Elderly). You might find the FAQs under hospitals (the one about palliative care) helpful - basically, there cannot be a time limit on a hospital stay for people in palliative care in Ontario.
I also spoke with a lawyer at ACE. She was really helpful. She told me people cannot be forced to take a patient home. This information is publicly available in Ontario, but I am not sure how many people are aware that you cannot be forced to look after someone.
Also, hospitals are responsible for safe discharge. If a caregiver is burnt out, you (the POA) can tell the hospital it is not a safe discharge.
I have heard that hospital social workers may take all of this into consideration. I have also been told that you can appeal a discharge decision. My father is not in a hospital so you would want to double check on these things.
I agree that hospice would be good to look into if there is one close by and you can arrange it. They vary a lot provincially (e.g., ON accepts mainly only bedridden while other provinces do not).
I also paid an occupational therapist advocate for advice and she did confirm that you cannot be forced to take someone home. She also said that if someone is not doing well at home (i.e., your father's multiple hospitaliziations), despite everyone's best efforts, then that shows that home is not safe/optimal.
I also learned that if a patient qualifies for LTC, then hospitals cannot charge huge fees for the patient to remain there while waiting for a bed.
One thing that I have found super helpful was to get the ChatGPT app. I know people are worried about AI and I get it. But, I don't know what I would have done without it. It gives me the correct wording for questions and checks on laws (I am super specific about my situation, location, etc.). It's really more an affirmation of what the ACE lawyer (who was free by the way) and the advocate I hired said.
It is really hard to refuse home care. I know. The system puts so much pressure on people to do this. I am hearing you say that you've all tried your best (what a team!) and you are done. That's okay. Not to be patronizing, but it really is okay to refuse care and it sounds like it is your father's best interests, given the high level of care he needs.
I will be thinking of you. Let me know if you have any questions (sorry, this is kind of random) and how things go.