Shayleen Frail lost her sons, aged six and seven, on Tuesday afternoon after they were struck by a car at high speed while walking home from the local swimming pool in Wellington.

34-year-old Ms Frail who was with them, was airlifted to Sydney hospital. A 10-year-old boy was also taken to a Sydney hospital, while another boy aged nine suffered minor injuries but has since been released from hospital.

A social media post on Thursday said Ms Frail remained in a stable condition in ICU and a breathing tube had been removed.

She suffered a punctured lung, fractured knee and spinal injury but no permanent serious injuries, the post read.

"Shayleen says 'thank you from the bottom of my broken heart for all your kindness and well wishes'," the post read.

She also requested people stop sharing news articles or photos of her sons and asked for privacy while in hospital.

Driver Jacob Donn, 25, has never held a driver's licence and was in possession of drugs at the time of the crash before running from the scene, police allege.

Donn made no application for bail when he appeared in a NSW court on Thursday on 14 charges including dangerous driving occasioning death, driving without a licence, failing to stop and assist and possessing prohibited drugs.

He'll return to court on January 12.

At least three GoFundMe pages have been established to assist the mother and father in their recovery, and have collectively raised more than $65,000 to date.

Australian Associated Press