They were also asked about the barriers they encountered as Māori to achieving those dreams.
Study author Eli Maiava reported the main hopes of the families were that their children would have confidence in, and strong connections with, their Māoritanga.
They wanted quality education and employment opportunities, and for their tamariki to be good people, living good lives.
But among the challenges they faced were limited and hard access to health and social services, and complex long-term health needs.
And in chasing their dreams for their children they also encountered racism and prejudice within the community and systems they relied on.
"Whānau feel like they are unwelcome in some spaces and unfairly judged, just because of the perception that it's held by others about their culture and identity,'' the researchers reported.
In the words of one interviewee: "I don't like going shopping here in (Hokitika) ... because I can't stand people staring at me.
"It's usually Pākehā and I feel out of place, walking around. I feel more comfortable going to Greymouth and doing my grocery shopping there."
Others who were not easily identified as Māori faced a different challenge when people assumed they were Pākehā:
"I've heard some stuff over the years that has been terrible and I'm like, 'whoa, mate, you're out of line! Where the hell are you getting this ... from?' and then pulling them up and they're like, 'What do you mean? Why do you care?' And I'm like, 'because I'm Māori!'"
Another interviewee had warned a son he would be judged as a Māori, and he had experienced that already.
"He had some money to go to McDonald's and get a drink before basketball training and he and his friend were stopped by the police and he was in school uniform and they said, 'Have you got anything in your bag you shouldn't have?' and he said 'no' and he ... handed his bag over and the police tipped it on the road ... on the footpath."
Racist attitudes shaped a young person's perception of their worth, the study noted.
They also made Māori less likely to engage with health and support services.
"Whānau feel they are regularly judged by others and looked down on by individuals and services, which impacts on their ability to access the resources and support that is available to them."
On a regular basis, whānau found it easier to go without than deal with the bias they knew they would face in the community, the researchers said.
Māori families on the West Coast relied heavily on one another in times of need; were resilient and all had ideas for ways to tackle the challenges they faced and help their tamariki.
The suggestions included respectful communication, consistent health professionals, well-funded mental health services, respectful communication and "better cultural training so we face less prejudice".
