The main plaintiff in the case, Cliff Robinson, who has spent the past 36 years looking after his two intellectually disabled children full-time, said he had been going through the process for more than a decade to get his work paid for and recognised.
More than 10 years ago he sent a letter to the Human Rights Tribunal about his situation, and has watched the case make its way through the courts since.
Mr Robinson and his 45-year-old daughter Marita and 42-year-old son Johnny - who both have microcephaly resulting in an intellectual disability - have been at each court case since the initial letter.
Today they had travelled to Wellington from Thames to hear the arguments at the Court of Appeal.
Outside court he said the families were not asking for much.
"All we're asking for is two, three, four hours a day [of payment], it's so simple," he said
"I can't believe they have gone through so much trouble trying to stop this."
Since the children's mother passed away in 1970, Mr Robinson has taken sole charge of looking after his two kids and said his day started at 5.45am and did not finish until 9pm.
But he said it was worth it and he knew what his children wanted and needed.
"The cuddle I give Marita in the morning a stranger cannot give."
He was adamant the families would win the case in the end.
"They can try all they like to stop it, but we will win this, it might not be here but it will come. It's part of the evolutionary process."
Green Party MP Catherine Delahunty, who was at court today to support the families, said the work they did for their disabled children was challenging and demanding.
"The families who care for their disabled children are not greedy people," Ms Delahunty said.
"All the carers want is the same amount that a stranger providing care for these families children would receive."
She said the Green Party obtained a breakdown of legal costs incurred by the Ministry of Health to appeal the decisions and found it cost $690,000 to defend the original case at the Human Rights Review Tribunal, $340,000 to appeal it to the High Court, and $70,000 to consider the High Court decision and deciding to appeal it to the Court of Appeal.
"The money the Government has spent on legal fees fighting these families could have been better spent paying for caregiving," she said.
The "thankless" work families with disabled children did was skilled full-time work.
"The best people to decide what happens are the family and the children who know what they need.
"The experts are in the family."
Health Minister Tony Ryall said he would not comment while the case was before the courts.
The Court of Appeal hearing is set down for two weeks.
