have talked him into spending almost all of his Social Security income a month, on a nursing home/rehab. facility.
It sounds as though you may be having difficulty with the social worker. Part of a social worker's role in a hospital setting is to help manage things like insurance, finding suitable facitlities that would be covered by his insurance, etc. All of that said, if he has medicare and supplements, he should be covered for a period of time.
I am neither an attorney nor a medical professional, but I can share what I learned based on personal experience and hope it helps you navigate through all this and know what to ask. In my mom's situation, she was in the hospital five months (mostly in ICU) before she passed. The doctors were never able to pinpoint the exact diagnosis. There were a couple of times that she started to do better and went to a step-down floor and even at one time went to an intermediate facility (a step between hospital and a rehab facility -- that lasted only a day before she had an episode that put her back in ICU at the hospital). Anyway, when there were times the doctors thought it was possible for her to survive the illness, we talked extensively about rehab facilities. Due to all of the nerve damage from the undiagnosed illness, she would have needed several months of painful rehab. In talking with the social worker, medicare, and her supplemental insurance company, I learned she would be covered up to a certain point. The point where she would no longer be covered is would have been the point where no further progress was being made and she was just in a stabilized mode. Since she never made it that far, it became a non-issue. Her case was also a little tricky because she was a nurse and had worked in several nursing homes before, and she knew which were good and which were not in her geographical area. With all the ***heck she went through in her illness and with being a great nurse, I feel she earned that right to be picky.
As for homecare, I will share my dad's situation. When he was dying, I had flown down to spend Thanksgiving with him (he was not in hopsital at that time). When I arrived, he was in such poor shape that I had to take him to the ER. (He was so sick that the stubborn strong man whom I loved to pieces put up no arguement when I asked him if I could take him to the hospital.) He was there a few days, and with healthcare being what it is, they needed to boot him to a rehab facility. I wasn't happy with this, and neither was he, but it was our only option. I helped in the transport to the facility. It was heart-breaking. His ward smelled of urine. As I helped him get settled in, it took often over an hour for a nurse to respond to a need (even urgent needs). He was there a week before he had a major medical incident that put him back in the hospital. When he was ready to be released back to the nursing home, he pleaded with all of his weak energy to not go back to the nursing home. He had been not only miserable in the nursing home but also even frightened (and we're talking about a very, very strong and brave man). My brother, extended family, and I worked it out for him to be released for homecare. We were fortunate in that one of my older cousins is a retired nurse who lived only a few miles away (so we didn't need to hire outside help). The biggest advantage of this was that he had folks taking care of his medical needs who knew him and loved him. He was released into homecare.
I share with you my mom's situation to hopefully give you information about questions to ask about insurance coverage for a nursing home. I share my dad's situation to hopefullly give food for thought. You might want to consider having a heart-to-heart conversation with your dad to understand his true desire - whether to rehab in a facility or to stay with you. You can't push him into anything (as long as he is legally competent), but if you sense that he may want to be at home, you can explain to him how care would be provided (whether through a home health worker or by you once you have been trained). You can lay out a plan for doctor follow-ups as appropriate, so that he is not frightened that you may miss a symptom that requires medical attention, etc.
Best of luck to you.