High Court Justice Cheryl Gwyn turned the application down, saying habeus corpus was not the appropriate way to consider allegations made by her mother when the case was still subject to Family Court and other High Court action.
Alice was born in late 2018 with health issues affecting her ability to feed and grow.
Oranga Tamariki removed Alice from the care of her mother and grandparents under a "place of safety warrant", after Jones took her home from hospital against medical advice in 2020.
Jutice Cooke said she was removed because health professionals developed concerns that "Alice's special needs are not being properly addressed in the care of her mother and maternal grandparents, and that this has put her in jeopardy".
During her first year, Alice was hospitalised a number of times and court documents reveal that Jones and her parents disagreed with health professionals about Alice's treatment, including the use of a nasogastric tube for feeding her.
At one point, after maintaining that Alice was not able to keep down a prescribed feed, Jones and her parents were using the nasogastric tube to feed Alice food they had put through a blender.
By March 2020, a doctor observed that Alice was "poorly nourished", had failed to develop normal feeding responses due to poor nutrition and that she still required nasogastric feeding.
When the doctor arranged a meeting of all involved in Alice's care, Jones objected to the presence of an Oranga Tamariki social worker and discharged Alice from hospital against medical advice.
Dr Nick Reid summarised the concerns that health professionals had about how Jones and her parents understood Alice's health needs and managed them.
He said in a report these included them not engaging or believing there was a problem with Alice's growth, not following recommended treatment plans, retracting or refusing consent for treatments, implementing "inappropriate feeding" without medical oversight, refusing to change treatments that doctors believed were unsafe, and refusing to agree to hospital admissions and a referral to the specialist Starship Hospital.
Another report prepared for the courts stated that the beliefs held by Jones and her parents "are so strongly held that it is unlikely they will follow advice of medical processionals as needed, and that this puts Alice at risk".
Meanwhile, Alice made good progress when placed in the care of her paternal grandmother, where a Family Court judge determined that she was "safe" and no longer needed the nasogastric tube.
That judge confirmed Alice's care arrangements with her father's family.
Jones then sought a judicial review of all of Oranga Tamariki's decisions in the case and filed defamation proceedings against Oranga Tamariki, Alice's paternal grandmother and two paediatricians involved in the girl's care.
All these applications were turned down in the High Court by Justice Gwyn.
Family Court proceedings to determine Alice's long-term care arrangements are continuing.
*The names given in the decision have been changed in the court documents to protect the child's identity.
