(CNN) The Phoenix couple who say police drew guns on them after their 4-year-old allegedly stole a doll are calling for the officers involved to be fired, saying their children are still traumatized by the experience.

The children are still "terrified, traumatized," Iesha Harper, the mother, said at a press conference Monday.

The couple has filed a notice of claim against the city for $10 million, which serves as a precursor to a lawsuit. In the notice, they say that the police incident began after they realized that their 4-year-old daughter had taken a Barbie-like doll from the store.

Harper said their daughter "wets the bed, wakes up in the middle of the night crying," and her 1-year-old won't let her go anywhere without her. "She's probably at home crying right now, waiting on me," Harper said.

In a 12-minute blurred-out video posted on the police department's Facebook page, one officer can be seen handcuffing Ames, first on the ground and then against a police car. The officer kicks Ames and can be heard yelling multiple times, "When I tell you to do something, you f****** do it."

Another officer appears to be pulling a gun on the passenger side of the couple's vehicle before Harper exits the car, holding a small child, with a second child by her side. Harper was five months' pregnant at the time.

"I was very much so afraid for my family's life and my life," Ames said. "I thought we were all going to be executed."

The Rev. Jarrett Maupin, a spokesman for the family, said they and others would be at a town hall Mayor Gallego called for Tuesday evening to hand over their written opinions "on what needs to happen."

The police said in a statement that the incident began when the Dollar Store reported shoplifting and directed police to people getting into a car. The police followed the car to an apartment complex parking lot, and an officer shouted loudly for the occupants to get out with their hands up.

Ames yelled that he did not do anything wrong and began to reach toward the center of the vehicle, causing the officer to draw his handgun, according to the report. Ames then began to comply and put his hands above the steering wheel, and he was then handcuffed, the report states.

The officer gave commands to Harper, still inside the vehicle, to put her hands in the air, but she refused, the report states. The officer feared that she was hiding something or was reaching for a weapon, according to the police report.

The report says that Harper was "loud" and "verbally abusive" and refused police commands.

Once they were both detained, Harper admitted that her aunt and her daughter had gone into the store, and when the child came out with a doll, she believed they had stolen it because they didn't have any money, according to the report.

In addition, Ames told police that he knew they had shoplifted from the store and that he threw a stolen pair of underwear out of the window, the report states. He, too, said he was sorry and that he was "very scared" during the incident, the report states.

The family said Monday the police report is "full of lies."

The doll was recovered and was returned to the store, the police report states. Because the stolen property was returned, store employees said they did not want to prosecute the case, so no one was charged.

No injuries to the man, woman or two children in the car were reported to police.

Authorities said the incident is under investigation.

"It was completely inappropriate and clearly unprofessional," Mayor Gallego said in a statement. "There is no situation in which this behavior is ever close to acceptable. As a mother myself, seeing these children placed in such a terrifying situation is beyond upsetting. I am deeply sorry for what this family went through, and I apologize to our community."

There is no body cam footage of the incident, Phoenix police Sgt. Tommy Thompson told CNN.

The involved officers are on desk duty pending an investigation. The police department has not named any of the officers involved.