My grandmother wants to be at home, how can I find her the care that she needs so that she can live at home?

She definitely cannot be alone; this having been determined by personal observation and by her doctor. Currently she stays with another family member. Although it has been discussed between the doctor and the family member currently overseeing her care that she may be in early stages of dementia, I wonder more about the possibility of her intentionally making messes in hopes of family members sending her back home, as she leaves stool on faucets and light switches. She doesn't do this while staying in her own home (under a family member's care).

If it is not safe for her to be alone 24/7, then it is going to be very tough and expensive to find an organization who will provide 3 people a day for an 8 hour shift. Home health is going to want her to have a certain level of independence before they are going to get involved. What does her doctor recommend?