Police have said the vehicle was being driven on the wrong side of the road and hit Harry head-on.
She said that if the diplomatic waiver was declined then she would take her case to Washington.
The death sparked widespread outrage after authorities revealed that Sacoolas claimed diplomatic immunity under worldwide law, allowing her to avoid prosecution and leaving British authorities and Dunn's loved ones to demand that she return to face the consequences of her actions.
Speaking on the BBC's Victoria Derbyshire programme, Dunn's mother, Charlotte Charles, said: 'If she had stayed. She's left a family in complete ruin.
"... We don't know how we can start to grieve for him..."
"Harry Dunn's family deserve justice", she added, "and in order to achieve this, a full and thorough investigation, with the assistance of all parties involved, needs to take place".
The U.S. Embassy spokesman said: "We express our deepest sympathies and offer condolences to the family of the deceased in this tragic traffic accident".
A spokesman for the US Embassy in London said: "Any questions regarding a waiver of immunity with regard to our diplomats and their family members overseas in a case like this receive intense attention at senior levels".
Defence expert Stephen Lanyard, a retired USA colonel, said: "Once a claim of diplomatic immunity is made and a person has left the country there is very little that can be done to bring them back".
Anne Sacoolas is a suspect in inquiries into the death of motorcyclist Harry Dunn in Northamptonshire on 27 August.
A fundraising page that was created to help the family with their quest for justice has attracted hundreds of donations, with more than £6955 ($13,600) raised so far.
The Prime Minister said that if the situation isn't resolved he will raise it himself with the White House.
Despite this, when police went to her home to tell her Dunn had died in the hospital, they found that Sacoolas had fled the country.
Police in Northamptonshire said Saturday, Oct. 5 they had been treating an unidentified 42-year-old woman as a suspect and that she had indicated she didn't plan to leave Britain.
"If we can't resolve it then... She's a mom", said Charles.
The crash took place in August outside RAF Croughton in Northamptonshire a U.S. intelligence hub in Britain.
She told Sky News: "This supposed fantastic relationship with the United States needs to be used to its full potential and Boris Johnson we would really appreciate your help".
"It's just about showing us that she's human and not. inhuman", Charles added.
Officers then sought to obtain a waiver from the USA embassy, which is required to allow for the arrest and formal interview of a suspect with diplomatic immunity.