Home health care versus hospice

My mother has dementia (moderate?) probably has anorexia, but other than that is okay.  Her vital signs are normal, she doesn't have cancer, heart disease, etc.  She is 90.

She had not been hospitalized since she was in her 70's (mastectomy).  My sister and I took her to emergency because she was losing a lot of weight and had a bad cough and she was admitted for testing.  It turns out all the testing was normal, she needed an anti-depressant, Aricept for dementia, antibiotics for mild bronchitis.  She took a nosedive in the hospital being out of her normal surroundings/structure (was hallucinating). 

I felt she should go home to the retirement hotel she lives in with my Dad, but with a caregiver, and home health. My sister and sons felt why not put her on hospice as the doctor (resident who saw her inpatient) suggested.  I went along with it, but not too impressed with the hospice care, and as she is really improving, I think home health would be the route to go.

With home health she can get physical therapy and occupational therapy if needed.  To me hospice is a wonderful program if someone is terminal.  My mother is improving, and I think it is a negative way of thinking.  Planning her death when she isn't "dying".  We did it that way, but now if her primary doctor agrees I want her in home health.  I got the power of attorney for health care for both of my parents.

My sister has been very nasty, abusive, I think possibly increasing prescription drugs she takes for anxiety, and I really don't feel she can make reasonable decisions, and frankly don't want to deal with someone who is so out of control emotionally.

Anyway, I'm taking my Mom to her primary doctor this afternoon.  The only advantage I can see to hospice at this point is that a nurse would come out at any time if an emergency arose, so she wouldn't need to be hospitalized.  Neither my sister nor I want her to be hospitalized. I think if necessary she could go to the ER (this may not happen for months, if at all), and released to home hospice.  She has end of life meds, oxygen, wheelchair,walker in her apartment if needed, but not needed at this time.  She is eating better, more alert, laughing, walking slowly but on her own.

Your thoughts on home health/hospice, and how to not engage with my sister when she gets nasty.