Harry Dunn's parents rejected a "bombshell" offer from Donald Trump to meet the woman accused of involvement in their son's fatal crash.
Charlotte Charles and Tim Dunn said they felt "a little ambushed" when the president revealed Anne Sacoolas was in the next room at the White House.
Mrs Sacoolas returned to the United States under diplomatic immunity days after the crash which killed Harry, 19.
Harry's parents said they wanted to meet Mrs Sacoolas, 42, in the UK.
Mr Dunn said a White House official told them she would not be returning to the UK, but Mr Trump said he would "try to push this from a different angle".
Harry Dunn died on 27 August when his motorcycle crashed with a Volvo near RAF Croughton in Northamptonshire.
Mrs Sacoolas - who is reportedly married to a US intelligence official stationed at the base - was interviewed by police but then returned to the United States after claiming diplomatic immunity.
That status has since been cast into doubt by the Foreign Office and Mr Dunn's family want Mrs Sacoolas to return to the UK.
Speaking on CBS This Morning, Mr Dunn said the president had suggested the meeting with Mrs Sacoolas "two or three times".
"We said no, we didn't feel it was right. He said 'she's here, let's get it on, get some healing,' something like that," Mr Dunn told the US TV network.
"There was a bit of pressure but we stuck to our guns."
In a separate interview, Mr Dunn said: "We didn't want to be railroaded into, not a circus as such, but into a meeting we weren't prepared for."
Ms Charles said they were "a bit shocked", adding: "The bombshell was dropped soon after we walked in the room that Anne Sacoolas was in the building, and was willing to meet with us.
"I don't think it would be appropriate to meet her without therapists or mediators in the room."
Family spokesman Radd Seiger described the White House meeting as "absolutely extraordinary" and "unprecedented".
But he said US National Security Adviser Robert O'Brien told the family during the meeting that Mrs Sacoolas "was never coming back" to the UK.
Ms Charles said she had told Mr Trump during the White House meeting: "If it was your son you would be doing the same as us."
She added: "He actually gripped my hand a little bit tighter and said 'yes I would be'. And that's when he said he would try and look at this from a different angle.
"I can only hope that he was sincere enough to consider doing that for us.
"He's the one in control here, but we're the ones in control of our situation as much as we can be - we still want justice for Harry and we will take it as far as we possibly can to ensure that that's done.
"We do feel that we have done as much as we can at the moment."
Ms Charles later told ITV's Good Morning Britain the family would "be forever disappointed, forever disgusted in both the UK and US governments" if Mrs Sacoolas did not return.
Mr Dunn said the trip to the White House "didn't feel like a stunt".
"I think the president was very graceful and spoke very well to us," he said.
"I genuinely do think he will look to resolve this in a way that will help us."
Over the weekend, Mrs Sacoolas broke her silence over Mr Dunn's death in a letter via her lawyers.
In it she said she wanted to meet his parents "so that she can express her deepest sympathies and apologies for this tragic accident".
Mrs Sacoolas was said to be covered by diplomatic immunity as the spouse of a US intelligence official, though that protection is now in dispute.
Northamptonshire Police said it would be submitting an evidence file to the UK Crown Prosecution Service "very soon".