You need to go to the IRS website and read about the difference between a W-2 employee and an independent contractor who receives a 1099 and decide which one of those your private caregiver is. I hire a private caregiver for my 23 year old son who has autism (I also take care of my dad who is 88) and I go the household employer route and pay FICA, Medicare and unemployment taxes because I schedule her hours and tell her what work to do with my son. I also withhold federal income taxes for her. If you go the household employer route, the IRS has a publication about being a household employer that helps you set it all up.
I am in Seattle, she will work out the hours with her family members, she and other sister will do care, it is 24 hour care, but I really do not have any involvement. She will have to make her own decisions on how to care for my Mom.