Final answer:
The nurse is acting as a Manager by directing family members to the hospital social worker to efficiently manage the situation and provide organized support.
Step-by-step explanation:
The role the nurse is assuming through the action of referring distant family members to the hospital social worker is that of a Manager. In this situation, the nurse is managing the resources and information flow to ensure the critically ill patient's needs are prioritized, while also addressing the family's concerns in a structured manner. The nurse is overseeing the coordination of care and utilizing the multidisciplinary team, which includes the social worker, to provide comprehensive support.