At his initial appearance in 2nd District Court, Judge W. Brent West appointed an attorney for Barney and set bail at $100,000. A status hearing is set for Sept. 3.
Barney himself called 911 to report that the girl was not breathing, according to a probable cause affidavit filed in court.
Police brought Barney to the Ogden Police Station, where he allegedly told police he lashed out at the victim because he was frustrated that the room was dirty, the other two children were misbehaving, and the victim was crying.
"Out of frustration, he punched her in the face twice," according to the affidavit. "After punching [the victim] in the face, he punched her in the stomach and squeezed really hard."
Barney allegedly told police that after attacking the girl, he left the room with the three children. While they were out, the girl was "lethargic and acting as if she was short of breath," according to the affidavit. The girl died in her stroller after they returned to the room.
Barney allegedly called the girl's mother, Kaci Rupert, who told him to call 911.
An autopsy performed at the Utah State Medical Examiner's office revealed that girl died of internal hemorrhaging caused by blunt force trauma to her abdomen.
The Utah Division of Child and Family Services took the other two children, ages 5 and 3, into protective custody.
Police did not release the name of the victim, who is referred to in court documents as K.L.