He hoped the appeal would give Emily's family some closure, he said.
"It'll just be nice to hopefully have a statutory conclusion and look forward to not having to think about it for 16 years," he told RNZ.
Turner has to serve 16 years before being considered for parole.
His parents, Leigh and Anita Turner, were convicted of perverting the course of justice by destroying a confession note from Turner and removing a jacket from the scene.
They were each jailed for 27 months.
Emily's family planned to sit in court during appeal proceedings, set down for a day.
They expected Turner and his parents to attend, said Mr Longley.
"We just really want to show them that we're still supporting Emily and very much supporting that justice goes down properly."
Mr Longley said Turner had not yet taken responsibility for what he had done.
"I think given the type of person he is, being so self-centred he was always going to have a tough time in prison but what's quite sad to us is he obviously hasn't accepted what he's done yet and he's not taking his punishment quietly. It would be nice if he just put his hand up, showed a bit of remorse and just got on with his sentence."