The 19-year-old motorcyclist died when his bike crashed into a car driven by Anne Sacoolas outside RAF Croughton in Northamptonshire on August 27.
Family spokesman Radd Seiger said on Twitter: "Yesterday the family were told the police had passed their file to the CPS (Crown Prosecution Service) yet tonight were informed that the police were travelling to the USA to interview Mrs Sacoolas.
"Those two statements appear to be contradictory on the face of it, further compounding the family's misery."
Harry's parents, Charlotte Charles and Tim Dunn, will on Tuesday meet with shadow foreign secretary Emily Thornberry, who is expected to call for a Parliamentary inquiry into the teenager's death.
On Monday, Foreign Secretary Dominic Raab told the Commons he had commissioned a review into immunity arrangements for US personnel and their families at the RAF Croughton annex in light of the case.
Mr Raab said there are "no barriers to justice being done" for Harry.
He also said the UK Government believes diplomatic immunity "clearly ended" for Mrs Sacoolas, 42, when she left the country for America shortly after the crash.
He added it would be for the CPS and police to decide what steps to take, telling MPs he is "not aware of any obstacle" under the UK/US Extradition Treaty.
Harry's parents have cancelled a meeting set for Wednesday afternoon with Chief Constable Nick Adderley of Northamptonshire Police after it became clear his intention was not to answer "a series of key questions" the family had prepared, Mr Seiger said.
The force's chief contacted the family to "provide clarity" that the meeting would only be a "private and personal visit to express condolences".
Announcing the decision to cancel the meeting on Twitter, Mr Seiger said: "The time for condolences has long since passed and the answers to the many questions about Anne Sacoolas's departure and next steps are long overdue!
"Every moment that passes without those answers only compounds the family's pain and misery. Totally unacceptable!"
Mrs Charles and Mr Dunn travelled to the US last week in an attempt to put pressure on authorities to return Mrs Sacoolas to the UK.
The visit included talks at the White House with President Donald Trump, during which the family was told that Mr Dunn's alleged killer was in a nearby room and prepared to meet them.
They refused, insisting such an encounter take place in Britain.