A Melbourne mother dressed four of her young children in nice clothing before driving her car "full bolt" into a lake, killing three of them, prosecutors allege.

Akon Guode, 36, appeared to be screaming as she entered Lake Gladman on April 8, according to a prosecution witness summary tendered in court.

Another witness, who called triple-0, said the car appeared to have been deliberately driven into the water.

"They have to fully mount the kerb, drive along a grass area and they - I saw them just drive full bolt, straight into the - into the water," Alexandra Colson told emergency services, according to the summary.

A third witness, Richard Allman, said he heard the sound of an engine revving.

He saw the car drive into the water "at a fast rate of speed", the summary says.

He then heard the sound of wheels spinning and water splashing and saw the car was a further 20 metres into the lake, according to the summary.

Guode was seen standing in the water outside the car screaming, but not doing anything, according to another witness.

Her one-year-old son Bol and his sister Hanger and her twin brother Madit, both four, were killed.

Guode and her six-year-old daughter Alual were pulled from the water.

The mother of seven has been charged with three counts of murder and one count of attempted murder.

She has not entered a plea.

The prosecution summary further says at the time Guode was being plagued by rumours, chased by debt collectors and $700 worth of Centrelink payments had been cancelled.

She owed almost $4,000 to gas and electricity companies, and Telstra, and was also sending money to her parents in Sudan, the court documents say.

She was planning to move to Morwell to escape rumours that had dogged her relationship with the father of her four youngest children, who was married to another woman, the prosecution summary says.

The day of the alleged murders, there was a rumour circulating that due to community pressure, the children's father, Joseph Manyang, was leaving Guode and moving back with his wife, the summary says.

Guode broke down in the Melbourne Magistrates Court on Tuesday as she begged to be released.

Relatives of Guode in the packed courtroom also began to cry as the accused killer sobbed and wailed in the dock, promising she would not go anywhere.

"Everything that you would tell me to do I would do, and I will not go anywhere," Guode said, sobbing, through an interpreter from the dock of the courtroom.

"I need some help so that I can go back home."

Guode will return to court on June 27 next year for a four week committal hearing, during which 46 witnesses will be cross examined.