Bay, your post had me crying and praying for you and your family. You are doing the best thing you can do. I worked as a hospice nurse for almost 4 yrs and loved every minute of it.
A nursing home is really limited as to what kind and amounts of meds they can give or how much staff time they can devote to a dying patient, but hospice has more liberty to dispense meds for comfort, more training on how to ease the pain and discomfort in the dying process and also staff that have nothing else to do but see your mother...they don't have to answer call lights or needs from other patients, just time for their hospice patient. I've sat at the bedside of a patient for 9 days straight and that's pretty common...the company I worked for stayed there at bedside until the very end so the patient was never alone. I loved that.
Every single patient on Medicare has hospice benefits available to them, so Medicare pays for both things at the same time...nursing home AND hospice care. There is no either/or on that billing. Hospice takes over providing end of life meds, oxygen services, briefs, and other medical equipment they need but the nursing home continues to provide the room, food, nursing care and nursing assistant care, all the while hospice provides nurses and nursing assistants as well. It's double the staff and double the individual care for a patient on hospice and you simply cannot get that by using a nursing home alone for end of life care.
I admire you so much for honoring your mother's wishes about this time in her life...not many have the courage to do so and will often impose their own feelings on the matter, delaying the end for their own benefit but don't often think of what their loved one is going through. Leaving this world is a precious time, much like coming into it, and it's wonderful when a person can get what they want at that time.

Praying that she is one moment with you and the next with the Lord. I've seen that moment happen in the eyes of a few patients and it was the most wonderful thing I've ever seen, the pure joy and light that shines from their eyes cannot be described.