Amanda L. Hamm, 27, did not enter a plea. Neither did her boyfriend, Maurice Lagrone Jr., 28, who is also charged in the case.
The children drowned Sept. 2 when the car they were in plunged into Clinton Lake.
Hamm and Lagrone are each charged with nine counts of first-degree murder.
Authorities have not said what they believe happened that day at the lake or why they believe Hamm's children were intentionally killed.
Authorities have not said how the car went down a boat ramp into Clinton Lake, and have not revealed a motive, other than that it did not involve life-insurance money.
Hamm asked for a court-appointed attorney. Lagrone told the judge he planned to hire his own lawyer.
Peters scheduled preliminary hearings in the case for Jan. 7 and kept their bond at $5 million. Both remained in custody.
They were arrested separately Tuesday and were being held on $5 million bail each, reports CBS News Correspondent Drew Levinson.
Deputies arrived at the lake in central Illinois on Sept. 2 within five minutes of receiving a 911 call from Hamm saying her children were in the water. The two suspects were on the lakeshore when rescuers arrived and Hamm was crying hysterically, according to one eyewitness.
Neither the couple nor investigators have ever offered a public explanation for why the couple was at the lake. Authorities have said the suspects were not launching or removing a boat, and it was not clear if they were in the car when it went in the water. The couple never spoke to reporters or returned messages for comment.