Yuhwei Chou of Skillman, Somerset County, is charged with two counts of first degree murder.
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The 36-year-old woman is accused of suffocating her 7-year-old daughter and 11-month-old son.
The victims' bodies were discovered bound and restrained in the back of a car that had gone off Mountain View Road in Hillsborough last week.
An autopsy revealed that 7-year-old Samantha Ross and 11-month-old Paul Ross died of asphyxiation.
Those in court say Chou showed no remorse during her hearing on Tuesday.
The court complaint said that Chou voluntarily stated that she had driven to Wawa for lunch and then True Value to buy duct tape and zip ties on November 8.
Next, she drove to Apex Park in Hillsborough and began to duct tape her daughter's face, but was scared by a bystander in the park.
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She then says she drove to Mountainview Road, in Hillsborough, and parked in a "hunting area" with a dirt driveway on the side of the road.
Chou then zip-tied Samantha's hands and duct-taped her face along with Paul's face.
She stated that she used her hands to suffocate the children until they were deceased.
Chou said in the complaint that she had been planning the two murders for approximately one week.
The following day, a person noticed the vehicle in the ditch of the road and told another person to call 911.
Chou was in the vehicle and had apparently zip-tied her own hands to the steering wheel.
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The children were pronounced dead at the scene.
Stories of a pending divorce and possible post-partum depression have been discussed as possible motives.
The judge said that Chou's attorney has the right to appeal, but that she will otherwise remain behind bars until her next court date on December 20.
Her bail was denied in part because of the nature of the crimes and concerns she could be a flight risk because she is not a U.S. citizen.
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