Becky Stephenson, a travel agent from Bradford, told how her customers were preparing to take off when they noticed a missed call from their son-in-law.
Mrs Stephenson told the Independent: "They were taxiing on the runway when they got the text message saying their grandson was in intensive care and they needed to get there.
"They passed the message to the crew, who spoke to the captain and he turned the plane back."
The pilot returned the plane to the boarding gate while staff organised the removal of their luggage.
Their grandson died the next day, and the couple said they were grateful to have had the chance to say goodbye.
According to Travel Mole, Becky said: "The pilot took the decision to return to the gate so the couple could disembark, but not only that, the crew also arranged for the couple to be assisted at the airport and they even got their car delivered from the car park.
"Every little thing you could think of, they took care of. Sadly my customers' grandson passed away the day after but had they not been allowed off the flight and had to fly back from Abu Dhabi they may not have made it to his bedside."
Etihad are also allowing the couple to re-use their tickets for a future trip to Australia.
Becky shared the story on Facebook and said: "I'm pleased that, via the power of social media, Etihad has got the recognition they deserve for their really excellent customer service."