But their QC told three Court of Appeal judges in London that they "do not seek a fresh inquest".
Hugh Southey, representing Mr Duggan's mother Pamela, explained: "The reason for that is that the inquest process was a traumatic process and not something the family would wish to have repeated."
What was sought was an order quashing the 2014 verdict.
Mr Southey argued that the coroner gave the jury an "unlawful direction".
He told the court: "No verdict is better than one based on an unlawful direction."
The QC said the family's case is that the verdict on Mr Duggan's August 2011 death was not "safe".
Mrs Duggan is challenging a decision by three High Court judges in October 2014 that the inquest jury was legally entitled to bring in its 8-2 majority verdict.
The jury decided in January 2014 that the 29-year-old was lawfully killed by a police marksman in Tottenham, north London.
Armed officers intercepted the minicab Mr Duggan was travelling in on the basis of intelligence that he was part of a gang and had collected a gun.
He was shot twice by an officer known as V53. One of the hits was fatal.
The jury concluded Mr Duggan, who jumped from the taxi, had dropped the firearm on to grass as soon as the minicab came to a stop - but the officer "honestly believed" Mr Duggan still had a gun at the time he was shot.
Mr Southey argued before Master of the Rolls Sir Terence Etherton, Lord Justice Davis and Lord Justice Underhill on Thursday that coroner Judge Keith Cutler and the High Court "fell into error".
Mr Southey said the coroner "directed the jury that the lawfulness of the lethal force, and the question of whether V53 was acting in self-defence, should be judged solely by reference to V53's honest belief as to the threat posed".
He added: "They were not told that, in deciding whether the belief was honestly held, they should consider whether or not that belief was based on reasonable grounds."
Submitting that the direction was unlawful, the QC said the coroner "failed to direct the jury to consider whether V53's belief was reasonable".
The judges will announce their ruling at a later date.
Additional reporting by Press Association.