How do you know ethically when hospice should come in?

As soon as the care for the dying becomes overwhelming to the care giver, it is time for hospice. It is not good for family members to provide care near the end because they can not think straight, nor care adequately for them. This is not good for the hospice patient. Why would a family member not want the health care professionals, who are trained in this area, not to care for their loved one, to be in the least amount of pain and suffering?