Harry Dunn was denied a chance to meet with suspects in their son's crash after Donald Trump dropped the "bomb shell" that she was in the next room in the White House.
Charlotte Charles and Tim Dunn felt "a little ambushed" by the proposal made by the US President.
Anne Sacoolas, 42, returned to the United States days after the crash in which 1
Harry's parents said they wanted to meet Mrs. Sacoolas in the UK.
Mr Dunn stated that a White House official had told them he would not return to the UK, but Mr Trump said he would "try to push this from another angle".
"We want to meet Ann Sakoolas, but we want to do it in the UK so the police can interview her," Mr Dunn added.
"We did not want to be involved not in a circus as such, but in a meeting for which we were not prepared."
Ms Charles said they were "a little shocked", adding: "The bomb was dropped soon after we entered the room that Ann Sacoolas was in the building and wanted to meet with us.
"I don't think it would be appropriate to meet her without therapists or mediators in the room."
Harry died near RAF Croughton in Northamptonshire on 27 August when his motorcycle crashed with Volvo.
Ms. Sacoolas – who is alleged to have married an American intelligence officer who was stationed at RAF Croughton – was interviewed by police but then returned to the United States after seeking diplomatic immunity.
Family spokesman Rad Seeger described the White House meeting as "absolutely unusual" and "unprecedented."
But he said US National Security Advisor Robert O'Brien told the family during the meeting that Ms Sakuolas "never returned." For the United Kingdom.
Ms. Charles said she told Mr. Trump during the White House meeting, "If he were your son, you would have done the same as us."
She added, "He actually squeezed his hand. me a little tighter and said “yes, i will be.” And then he said he would try to look at it from a different angle.
“I can only hope that he was sincere enough to consider doing this is about us.  "He is the one who controls here, but we are the ones who control our situation as much as we can, we still want justice for Harry and we will take it as far as it is possible to ensure that this is done.
"We think we've done as much as we can right now."
Ms Charles later told ITV on Good Morning Britain that the family "would be forever disappointed, forever disgusted with both the UK and US governments" if Ms Sacoolas did not come back.
Mr Dunn said the trip to the White House was "not" I don't feel like a stunt. "
"I think the president was very graceful and spoke very well with us," he said.
"I honestly think he will look to resolve this in a way that will help us."
Over the weekend, Ms. Sacoolas broke her silence on Mr. Dunn's death in a letter through his lawyers.
In it, she said she wanted to meet his parents "so that he could express his deepest sympathies and apologies for this tragic catastrophe."
Ms. Sacoolas is said to be subject to diplomatic immunity as the spouse of US intelligence, although this protection is controversial.