Final answer:
The appropriate action for the care manager is to refer the family to a home healthcare agency that can provide the necessary services for the child's care.
Step-by-step explanation:
The appropriate action for the care manager in this situation is to refer the family to a home healthcare agency that can provide the necessary services for the child's care. Home healthcare agencies have trained professionals who can provide 24-hour care to ventilator-dependent clients with tracheostomies. These professionals can assist with ventilator management, tracheostomy care, and any other needs the child may have.