Her father Henry Dare, also known as Sunday, has said that his grandson is "definitely" the boy in the Isis video.
Mr Dare, a minicab driver, told the telegraph.co.uk: "I was surprised when I saw the picture. It's definitely him. Of course I'm worried but there's nothing I can do now. I'm not angry - I would never have expected it. I just hope someone is trying to bring them back."
And in an interview with The Sun, he begged his daughter to return to Britain. "Grace, Grace, come home with my grandchildren. Come home, we love you, come and face the music."
In 2014, Grace Dare posted a shocking photograph to her Twitter account of her then four-year-old son Isam smiling as he aims an AK-47 rifle.
She is married to a Swedish Islamic fighter called Abu Bakr, and is a convert who previously attended a mosque in South London.
Isa also has at least one younger sibling, a boy who would now be between two and three years old, who his mother has referred to as a "mini mujahid", or holy warrior.
Dare is believed to have been radicalised online before she started attending the Lewisham Islamic Centre, where the kilers of British soldier Lee Rigby are said to have worshipped, although the mosque denies they were part of the congregation.
Jihadi John's successor
The other figure in the video has been dubbed the "new Jihadi John", due to his similarities to the infamous voice and face of Isis's previous execution videos.
British jihadi Mohammed Emwazi, who was filmed executing six men including British aid workers David Haines and Alan Henning, was killed in Raqqa, Syria, in November by a missile fired from a drone.
His appearance comes at the end of the latest propaganda video which appears to chillingly introduce a new "Jihadi John" figure.
His successor appears to direct one comment at potential recruits, criticising those who "wish to continue fighting under the banner of Cameron on the minimum wage." At the end of the rant the man shoots the prisoner in front of him at point blank range, as the other four men are also murdered.
British security agents are trying to identify the militant, with speculation mounting that he could be Siddhartha Dhar, a British jihadi who fled to join the terror group in Syria while on police bail in 2014.
Dhar's sister Konika has said the voice in the video sounded "a bit like" her brother, but she did not believe it was him.
Ms Dhar, from North London, said: "If it is him, bloody hell am I shocked? I am going to kill him myself. He is going to come back and I am going to kill him if he has done this. I can't believe it. This is just so shocking for me. I don't know what the authorities are doing to confirm the identity, but I need to know if it is."
His mother today said she could not be sure of it was her son but was shocked by the revelations, and never suspected he had terrorist links, describing him as 'sensitive and shy'.
His mother Sobita Dhar said: "These are the most difficult questions to answer - I just cannot say. I'm not sure within myself whether it's the truth or not. I last saw him before he went off to Syria two years ago."
The father-of-four from Walthamstow was one of nine men detained on suspicion of encouraging terrorism and supporting the banned group Al-Muhajiroun.
The former bouncy castle salesman later posted a picture of himself cradling his baby while brandishing an AK-47 to taunt security services whose blunders allowed him to escape.
Dhar, also known as Abu Rumaysah, is believed to have met, and possibly mentored, Michael Adebolajo, one of the murderers of Fusilier Lee Rigby.
Terror expert Raffaello Pantucci, director of international security studies at Royal United Services, also believed the executioner's voice sounded like Dhar's.
He said: "He sounds a bit like Abu Rumaysah from Al-Muhajiroun videos. From watching him in Al-Muhajiroun videos and this new video he sounds very similar. The masked man sounds like he is from London. ISIS is full of people who are from all over the place, but he seems educated, given he uses the word 'imbecile' a number of times."
