Can we hire private caregivers and give them a 1099 at the end of the year?

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.

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.