The children 11-year-old Jaylee, nine-year-old Matika and eight-year-old Zahara have not been heard from since.
Ms Heuston, a mother of seven, is believed to have contacted a welfare worker on Friday afternoon and police are pleading with her come forward.
“She’s made some threats in relation to what her behaviours might be at the present time.”
Ms Heuston’s phone is off and she has not touched her bank accounts.
She was listed as a missing person on Friday and police are concerned for her welfare.
Her former partner Jason said he has grave concerns about her mental state, given that she has been displaying threatening and erratic behaviour, according to Channel 7.
She is described as being approximately 155cm tall with a thin build, long brown hair and blue eyes.
Ms Heuston is believed to be driving a grey Mitsubishi Magna, registration XHB184, and is known to frequent the Rockbank, Preston, Glenroy and Hatfield areas.
Police have released images of the children and mother in the hope someone may recognise them and contact police.
Ms Heuston is believed to have lost weight since the image was taken, so may appear different.
Anyone who sees Jaylee, Matika or Zahara is asked to contact Greensborough Police Station on 8432 0200.