Meanwhile, a local judge has issued a gag order on authorities investigating the deaths.
Laney, 38, was being held at Smith County Jail in lieu of $3 million bond on capital murder and aggravated assault charges.
County sheriff's officers arriving at Laney's home early Saturday found two of her sons, 8 and 6, dead and a 14-month-old son alive but bleeding in his crib with a pillow over his face.
"She was approximately 100 yards behind the house, still in her nightclothes, blood all over her," Sheriff J.B. Smith said on the CBS News Early Show before the gag order was imposed. "She had evidently beaten them to death with a rock — led them out of the house one at a time, and killed the children."
Aaron James Laney, the youngest of the three, remained in critical condition early Monday at a Dallas Hospital.
Laney's demeanor on Sunday was described by Smith as erratic during interviews with investigators.
"Sometimes she is incoherent, sometimes she's in a fetal position and sobbing. Sometimes she's singing spiritual hymns or muttering about God and sometimes she has a flatliner (poker) face and not saying a thing during interviews," said Smith. "But she has not spoken of the crime anymore. She said it all on the 911 tape. She said she had killed her children."
The sheriff said that Laney used her cell phone to report that God ordered her to kill her sons.
"The judge clearly was concerned that there would be absolutely no hope for a fair trial for Laney if the police in Tyler continued to offer public comments about what happened over the weekend," says CBSNews.com Legal Analyst Andrew Cohen. "Now, it already may be too late but at least for now there ought to be no more interviews describing what did or did not happen at that home."
Sheriff's deputies arriving at the residence in New Chapel Hill found Joshua Keith Laney, 8, and Luke Allen Laney, 6, dead in the yard wearing only their underwear. Large rocks were found on top of their tiny bodies.
Wearing bloodstained pajamas, their mother told the first deputy on the scene "I had to" when he took her into custody, according to an arrest affidavit obtained by the Tyler Morning Telegraph.
"This is already a capital murder case and if the initial reports are accurate the real battle at trial, if there is a trial, won't be over whether this mother killed her children but whether she was legally insane at the time," says Cohen. "And as we know from the Andrea Yates murder trial last year, the law in Texas makes it virtually impossible for that sort of defense to prevail."
Andrea Yates of Houston confessed to drowning her five children in a bathtub in June 2001 and was convicted of murder. The jury rejected defense pleas that Yates was innocent by reason of insanity. She was sentenced to life in prison and is not eligible for parole until 2041.
"The big question now will be whether anyone inside or outside of the prosecution's office thinks the defendant was legally insane at the time of these killings — a very tough standard in Texas," says Cohen. "Everything in this case will follow from that diagnosis and if there are differing diagnoses about that we'll likely see them played out in court at trial."
Meanwhile, First Assembly of God Pastor Gary Bell told his congregation Sunday about the deaths of his two nephews, injuries to the third and the arrest of his sister-in-law.
"No one would have expected such a tragedy to unfold, especially so close to home," Bell said during the service. "This family was the last one you would think this could happen in."
"She was just a stable individual in society, well-respected, well-loved, very gentle woman — no indication of anything like this," said Smith.