The family of a British teenager killed in a wrong-way crash involving the wife of an American diplomat said President Donald Trump dropped a "bombshell" during a meeting at the White House, revealing that the woman was waiting to meet them in the room next door.

Harry Dunn, 19, was killed after his motorcycle was hit by Anne Sacoolas, who admits driving on the wrong side of the road near a British military base used by the United States.

Sacoolas, 42, whose husband is an American diplomat assigned to the United Kingdom, said she cooperated with the police but flew back to the U.S. three weeks later.

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The case has sparked a transatlantic dispute about whether she still has diplomatic immunity from prosecution.

Harry Dunn's parents say they want justice for their son. Courtesy of the Dunn Family

Dunn's parents want Sacoolas to return to the U.K. to face trial, and they have traveled to the U.S. to find answers. But during a meeting with Trump at the White House on Tuesday, they said the president made what they considered a shocking and inappropriate offer.

"The bombshell was dropped not soon after we walked in the room: Anne Sacoolas was in the building and was willing to meet with us," Dunn's mother, Charlotte Charles, told reporters in Washington afterward. "We made it very clear that as we've said all along … we would still love to meet with her but it has to be on our terms and on U.K. soil."

Mark Stephens, a lawyer for the Dunn family, told Sky News on Wednesday the plan of the Trump team was to set up the meeting and then "bring in the press corp to show it was all happy families."

"Unfortunately, that was a gargantuan miscalculation," he said, describing the way the meeting was proposed as "so wrong."

Stephens also described Sacoolas as a "fugitive from justice."

Dunn's father, Tim Dunn, had said earlier that Trump was "very gracious and respectful" throughout the meeting, holding Charles' hand at one point and promising her he would seek a solution. "He was understanding and I think he genuinely will look to try and resolve this," he said.

But Charles, the teenager's mother, said the meeting ultimately went "round in circles" as Trump and his team tried to get the family to "accept the invitation to meet her [Sacoolas] on their terms which we weren't willing to do."

She said that any meeting would need to involve "therapists and mediators in the room and not just her and us. I wouldn't imagine that's even advisable for her, let alone us."

Tim Dunn said they felt "a bit rushed" and that they "don't think it would have gone too well" if they had gone through with the president's plan.

Charlotte Charles and her husband, Bruce Charles, arrive for a news conference in New York on Monday. Carlo Allegri / Reuters

Sacoolas has admitted that she was driving on the wrong side of the road when she hit Harry Dunn on his motorcycle near RAF Croughton in Northamptonshire, England.

"Anne was driving on the wrong side of the road and had no time to react when she saw the motorbike approaching — the crash happened too fast," according to a statement from her family's legal representative, Amy Jeffress.

She stayed at the scene of the accident but was told by British police that she should go home and that they would call her, Jeffress said. They never did, and three weeks later the family flew back to the U.S.

"The U.S. authorities determined that it would be difficult for the couple and their children to remain in the small Croughton community under these tragic circumstances," Jeffress said.

Trump initially ruled out Sacoolas returning to the U.K., but later in the meeting Tuesday he mentioned trying to "push this from a different angle," Dunn's mother said.