The thieves took a laptop, mobile phones, cameras and iPods - which had all been stored out of sight - and the family's luggage, which they now have to replace to get their gear back home.
They also took a hard drive with irreplaceable footage of Ms Ives' late mother.
"My mum passed away - it will be two years in November - after quite a short illness of cancer. Before she died, we recorded her speaking about us as children, and there were also photos of her on the hard drive. That's stuff we obviously can't get back.
"That was one of the reasons we came here. The past couple of years have been a bit of a shock and unexpected. We came to New Zealand with mum in 2006 and it was a country we all fell in love with. We thought it would be a really nice experience to come back with dad."
Ms Ives called the police, who told her that other campervans parked in the area had also been hit.
Senior Sergeant Ross Endicott-Davies said campervans were always targeted by thieves.
"It's been very much on our radar, but it's not epidemic proportions," he said.
"Any campervan parked on the side of the road at this time means 'tourist' [to thieves]. Irrespective of whether it's the World Cup or otherwise, they do tend to be targeted, even in remote country areas."
He said police patrols were concentrating on areas where campervans were parked and were keeping a close eye on any they saw sitting in residential streets.
"Campervans stand out, so obviously we're looking at those. We've also identified hot spots and we've got a heightened presence around those."
Mr Endicott-Davies urged people to lock their valuables away.
"Obviously it's slightly different with campervans because people can't take all their stuff with them. But don't leave valuables in the vehicle as much as possible."
He said that rather than parking on a street, people should leave campervans in designated areas.
There are a number of parks in the city, including Alexandra Park, where people can pay a fee to leave their campers and get a free shuttle to matches at Eden Park. The sites are patrolled by security.
Ms Ives urged people to take up the offer of a secure park.
"In hindsight, it is something we really wish we'd done. Pay that bit of money to hopefully ensure a bit more security," she said.
"Unfortunately, our trip has been a bit tainted. We still love the place and everyone's been fantastic. It just put a bit of a dampener on the amazing hospitality and fantastic show that New Zealand's put on for the World Cup."
CAN YOU HELP?Contact the police if you have information on the Ives' stolen hard drive.
