The way your trip insurance defines a medical emergency may have a significant effect on your family.
MORE INFORMATION FROM U.S. Department of State: Travel Medical Insurance Providers
A consumer purchased insurance through his credit card company and believed it would cover medical emergencies experienced during their travels abroad. Unfortunately, his wife fell and broke her hip. He contacted the insurance company about having her transported home for the required surgery on her hip. The insurance company told him the policy specified she would be taken to a facility that provided "adequate" medical care. The company told him that the level of care in the country they were visiting met that definition.
He did not agree with the company's assessment of the level of care and opted to fly his wife home at his own expense. The point of this story, make sure you understand exactly what is covered in your trip insurance.