When security guards confronted them, authorities say Frye and the other two adults fought with the guards.
The Burtons and Frye told the judge they were indigent. The children are in the custody of a relative who lives in Cleveland.
The group is also accused of identity theft, and police in both Chicago and Cleveland are trying to find the victims.
The Chicago mother, along with her boyfriend and his mother, were all in jail in Ohio Thursday. Police arrested them this week in Parma, which is about nine miles south of Cleveland.
Police say the shoplifting ring involved the mother's two children, and one detective called the scheme pathetic.
Parma police say Frye's 10-year-old daughter helped her 8-year-old brother steal a handful of expensive, designer hats with their mother's approval. At least one alleged theft was caught on surveillance tape.
"It's obvious from the video that mom knew what the kids were doing," said Detective Marty Compton, Parma police. "I mean, the kid walks up within four feet of mom, the sister, in plain view of mom, hands him a shopping bag, and he stuffs $225 worth of hats into it."
It took place at a Macy's store in Parma, Ohio. Police say the 34-year-old mother is just one link in a shoplifting ring.
When the store's security guards confronted Frye, police say she got into a fight with them, and another suspect - 64-year-old Diana Burton - jumped in as well. Authorities say Burton's son, Donald Burton, who is Frye's boyfriend, punched one security guard in the face.
"These three all have identification that hands them back to Chicago, and Diana Burton has a history that gives us 32 aliases," Compton said. "So they've been around the block before."
Following the fight, the three adults and two children left the store and were about to take off in a 2009 Chevy Suburban. Police say they arrested everyone on the spot. Inside the vehicle, Parma detectives say they found credit cards, gift cards and what's believed to be stolen property.
"As the result of the arrest, we've determined that we can probably ties these people to crimes in Chicago and Cleveland and God only knows what points between," Compton said.
Parma police say there could be dozens of victims. They've already identified four alleged victims in Chicago.