What care restrictions does hospice have if home care is provided by family members 24/7 & 2 people during her waking hours?

We want mom w/Alzh. 6th stage pretty much, to be home from Rehab but they will not release her. Hospice of CNY in Liverpool said we just have to tell Rehab we want hospice. Will hospice allow us to help mom exercise & take her regular meds as she did before hospitalization & rehabilitation? We will have 24/7 care @ home for her. We will not insist if she refuses to get up, exercise or eat. How is hospice paid for? We have all equipment mom would need at home care. Dad still lives @ home but couldn't care for mom. Siblings & hired help would provide 24/7 care. Dad lives in own house with mom until mom got sick & ended up in rehab. Only thing we we'd need from hospice right now is 24/7 on call nurse. We don't know how long mom will live. Originally Dr.recommended discharge w/hospice.