Would you, as a labor and delivery nurse, honor a patient's request to delay a medically necessary intervention, such as an emergency C-section, to allow a family member to arrive at the hospital?

This typically is not up to us as the RN. If it really is an emergency the MD should consent the patient and express the urgency of the situation. If the patient wants to wait for a family member they can refuse the procedure and sign that they are refusing the procedure against medical advice.