I'd had this same hospice organization with my dad's care, and they were superb. Hospice and the nursing home worked seamlessly together to give my dad the best care possible.
He had his familiar nurses and aides, because he remained in the home where he'd lived since his brain surgery left him with severe dementia. However, he also acquired expert hospice nurses, a counselor and a second chaplain (this choice is optional). Who can get too much love and support?
Much-Deserved Pain Relief
For Mom, the situation was much the same. From the time hospice took over, Mom was out of pain for the first time in years. Hospice gave her a bone cancer drug which gave Mom nearly complete pain relief for several weeks.
As her condition grew worse, more medication was added, but Mom was content and no longer pleading to die. A couple of months later, Mom died peacefully, happy to join Dad.
In both cases, I'd have liked to have called in hospice a bit earlier, but the nursing home was doing a fine job, and you do have to have a terminal diagnosis before hospice can join the care team.
That diagnosis was up to the doctor. The nursing home staff helped me with the paperwork so the doctor had what he needed for the diagnosis and we were finally able to make the call.