It's impossible for anyone to put themselves in your shoes. Most though that know you somewhat realize you are not ok at all. You need self care at a time like this. I don't mean to be harsh, but you do realize that your own health, physically and mentally, needs to be first. You won't be there for him if you continue to be sleep deprived, you could have an accident. Just an example. I care about you very much.
My own mother a year ago, went from hospital to rehab, to home, to hospital. It was exhausting driving there, but yet I had support from my brother. One day, I was sleep deprived and he thought she was passing. I drove crying to the hospital, praying not to take her yet. I understand how you want to be by his side. I just believe that God would have taken care of her, and in the end I believe he did. I was there, and it was so difficult to be helpless wanting to help her. Yet I'm still not sorry for staying with her until she passed. I so understand you don't want the last days to be in hospital or rehab. I pray the best outcome for you both.

Please do whatever you need to do to rest at times between visits with him.