Tanasia Perry, 28, of Adams Road, was charged with two counts of endangering the welfare of a child in the Wednesday night incident, which occurred about 9:40 p.m., when police said the outside temperature was about 28 degrees.
Police said they believed the children had been left alone for about half an hour.
At her arraignment before Judge Tricia Ferrell in First District Court in Hempstead Thursday afternoon, Perry was ordered held in custody. Her next court date is Monday.
"An 11-year-old basically watching a 14-month-old in a car in those temperatures, 28 degrees, with the exposure to hypothermia, I would certainly think that would constitute endangering, so we're very satisfied the charges are appropriate," said Det. Sgt. Anthony Repalone, a Nassau police spokesman.
During a news conference at police headquarters, Repalone said the children were discovered by two passersby who called police.
Repalone said Perry returned and spoke to officers on the scene and admitted to leaving the children alone for some time, believing it was not longer than 15 minutes. He said police estimate she was gone for at least 30 minutes.
"The children weren't experiencing any hypothermia but potential, obviously, for that period of time, the risk was there," Repalone said.
The children's father picked them up and has custody of them now, Repalone said.
"Unfortunately these things do happen on occasion," he added.