The couple had kept their mobile phones switched on after they boarded the plane because they "suspected something was wrong", Ms Stephenson said.
Once they got the text confirming the terrible news, cabin crew quickly stopped the plane from taxiing so the couple could disembark.
The crew also unloaded the couple's luggage from the aircraft, escorted them to the terminal, and arranged for their car to be collected so they could rush off to the hospital.
The couple made it in time to see their grandson, who died the next day from an undisclosed condition.
Ms Stephenson said Etihad went "above and beyond" to help her clients during the gut-wrenching emergency.
"Every little detail (was) thought about and taken care of," she wrote in her Facebook post.
"Had they (the passengers) not been allowed off the flight and had to fly back from Abu Dhabi, they may not have made it to his bedside."
Ms Stephenson said Etihad also told the couple they could re-use their flight tickets at a later date.
Her post sparked a wave of praise for the airline, with many saying it was "truly amazing" and the story "heartwarming".
Although airlines and flight crew often bear the brunt of our travel frustrations, there have been other examples of pilots and flight attendants going way beyond the call of duty for passengers in a pickle.
In December, a Delta Airlines pilot was hailed a hero when he turned his plane around to pick up a family who were close to missing their father's funeral.
The family had been left stranded at the gate at Minnesota's Minneapolis-St Paul International Airport after their connecting flight to Tennessee - where the father was to be buried - was delayed.
The pilot spotted the distraught family from his cockpit and held the flight so they could board and get to the funeral in time.
In another act of awesomeness, when a Delta flight from Philadelphia to Atlanta in May last year was diverted to Tennessee due to storms, cabin crew ordered pizza for everyone on board.
Twitter quickly became inundated with snaps of flight attendants handing out boxes of hot pizza to grateful passengers, although it wasn't the first time that happened - apparently the pizza delivery is part of Delta's company policy in such situations.
And in another legendary example in December, an EasyJet pilot wrote 32 notes of absence for students whose flight from Cyprus to London Gatwick was delayed for 20 hours, causing them to miss their classes.
The children had spent a week in Cyprus with their parents when heavy fog caused them to arrive in London a day later than expected.
Even better, pilot Captain Wayne Mott's notes for the children's teachers could not have been cooler.
One note, addressed to the teacher of eight-year-old Joshua Skuse, read: "I am very sorry that Joshua was not at school today. He has been involved in a secret mission in the Eastern Mediterranean Sea at very short notice.
"We hope that this mission will soon be complete and that he will see you bright-eyed and bushy-tailed on Tuesday morning."
The note was so well received Captain Mott scored an invitation to be a guest speaker at Joshua's school.
