A spokesman for the teenager's family said they would only be satisfied if Mrs Sacoolas agreed to return to Britain and face the full legal process.
The family will initially spend time in New York City fulfilling a series of media interviews before travelling to Washington to meet US officials.
Their trip comes as Dominic Raab, the Foreign Secretary, confirmed in a letter to the family that Mrs Sacoolas no longer has diplomatic immunity now she has left Britain.
But legal experts have insisted that if Mrs Sacoolas had diplomatic immunity at the time of the accident, that protection from prosecution would still exist if she were to return.
Geoffrey Robertson QC, who is the family's barrister, dismissed Mr Raab's intervention and called on the Government to support the family in bringing a civil case against Mrs Sacoolas in the United States.
He said: "Of course it should have been obvious to the Foreign Office from day one that diplomatic immunity does not apply once she has left the country.
"She could be sued for negligence in the United States and the Foreign Office should make funds available for the family to do so if that is the only way to provide them with some measure of closure and justice.
"On the other hand, if Mrs Sacoolas is genuinely contrite, she has the right, no matter how much pressure is placed upon her by the State Department and the CIA, to follow her conscience and come back to Britain to face possible prosecution."
Northamptonshire Police are expected to hand a file on the accident to prosecutors this week.
But experts have said the thorny issue of the diplomatic immunity will need to be resolved before any charges can be considered.
Lawyer, Edward Grange, a partner at Corker Binning, specialising in extradition, said: "In order to apply for extradition the Crown Prosecution Service would need to be in a position to charge her and they will not be able to do that if she does have diplomatic immunity."
He said even if it were proven she did not have diplomatic immunity extradition might still be problematic.
He said another option open to the British authorities would be to apply for Mrs Sacoolas to be added to the Interpol red list, which could leave her open to extradition proceedings if she were to travel to another country outside the United States.
The mother of Harry Dunn has rejected an apology from the woman suspected of involvement in his fatal car accident, saying "sorry doesn't cut it".
Harry, 19, died when his motorcycle was hit by a car allegedly driven by Anne Sacoolas, 42, the wife of an American intelligence officer based at RAF Croughton in Northamptonshire on August 27.
Mrs Sacoolas, who claimed diplomatic immunity and left Britain following the accident, has now written a letter expressing her "deepest sympathies and apologies" and offering to meet Harry's parents.
But Ms Charles said: "My opinion on Anne Sacoolas now wanting to come forward and say sorry - to be perfectly honest, yes it's the start of some closure for our family.
"Having said that, as it's nearly seven weeks now since we lost our boy, sorry just doesn't cut it.
"That's not really quite enough. But I'm still really open to meeting her, as are the rest of us. I can't promise what I would or wouldn't say, but I certainly wouldn't be aggressive."