Final answer:
The best nursing diagnosis problem statement for this family would be: Grieving related to the terminal illness diagnosis of a family member.
Step-by-step explanation:
The best nursing diagnosis problem statement for this family would be: Grieving related to the terminal illness diagnosis of a family member. Grieving is a normal response to loss, and in this case, the family members are experiencing sadness and tearfulness since the diagnosis was given. By acknowledging their grief, the nurse can provide appropriate support and interventions to help the family cope with the challenges they are facing.