First of all hospice care can be done at home. My Dad went through it . . . twice. Yes, he was in the same position as your Dad, told he was in end stage heart failure, had weeks to live. They started him on hospice care. Amazingly enough, the hospice nurse was able to monitor his medications closely enough that my Dad stabilized and was taken off hospice after 6 months (the limit). He lived almost 2 years from that first diagnosis. What really ended his life was lung cancer that spread through his body. Again, hospice people were there at home to keep him comfortable with meds, company, bathing, hospital bed and such near the end.
Really, we couldn't have done all that care alone. They taught us so much but it was exhausting.