Disaster befell the family almost as soon as they arrived though, Mrs Amin suffering a heart attack soon after arrival in Canada and then being diagnosed with cancer.
Restricted by the conditions of her visitor's visa but desperate to care for her parents, Zhian and her young daughter stayed in Canada as long as they could but were eventually obliged to return to New Zealand or face deportation.
Her parents' medical status meant doctors advised they should not fly and Zhian was forced to leave them in Canada.
Back in Dunedin, she has frantically sought help from the Ministry of Foreign Affairs and Trade, local MPs and Canadian officialdom, and has also written to Prime Minister Jacinda Ardern.
"I just want someone to help," Zhian said.
"A lot of people have been involved, but no-one has been able to help us."
The family's travel insurance covered their initial expenses but has now run out.
The operation Mrs Amin now needs to be able to travel is not covered, and the couple's conditions meant they remained in limbo, unable to continue their travels to Iraq and unable to return home.
"Also I cannot go back, at the moment [because of concerns about obtaining a visa] they will not let me back in to Canada," Zhian said.
"When we left, we had online automatic visas, but they still kept us in the airport for eight hours' interrogation, despite my New Zealand passport and the fact I had not come from Iraq ... they only gave me two months to stay there."
Zhian's letter to Ardern asking for help received a sympathetic response and a promise to forward her case to Mfat, but she has yet to receive a reply from the ministry.
Whether her parents travel on to Iraq or come back to New Zealand does not worry Zhian - she just wants to be reunited with them, be that in Canada or elsewhere.
"They need to be out of the situation they are in," she said.
"Mum needs surgery and until it is done she can't fly ... Dad needs care for his dementia, but without me there he is in the hospital with Mum and soon after I left he went into a coma ... I want to be back to see them as soon as possible."
An Mfat spokesman said the ministry was aware of Zhian's parents' circumstances, but would not comment further.
"Due to privacy considerations we are unable to provide any further information."
However, the ministry noted New Zealanders stuck overseas could be expected to pay any medical costs themselves.
"This includes any costs involved in returning to New Zealand, which could involve special flights and a medical escort."
