According to the Gwinnett County Police Department, officers were called out to Alexander Park in Lawrenceville, Ga. at around 6 PM on Sunday ... following reports of a domestic dispute. Once they arrived, cops say a woman told them an unknown male, later identified as Moore, had shot at her car.

She also, according to police, said an unknown woman slashed her tire with a screwdriver during the incident as well.

The woman, police said, explained to officers that everything had started after her 9-year-old niece got into a tiff on the playground with Moore's young daughter.

According to police documents, the woman told police an angry Moore approached her and told her he was "going to get his niece to come and fight her" over the kids' altercation.

Police in the docs said the woman tried to leave in her car to avoid conflict ... but Moore blocked her in her parking spot with his vehicle. That's when cops say the unknown woman started puncturing her front left tire with a screwdriver.

Cops say the woman told them she tried to leave, but accidentally struck Moore's car ... and that's when she claims Moore shot at her ride while her niece and son were in the back seat.

According to the police report, the bullet struck the woman's driver's side door ... but thankfully, no one was injured.

The incident was apparently caught on video, and in the footage ... it looks like you can see Moore and a woman near the victim's car before a gunshot rings out.

Police said they later stopped a vehicle at the park matching the description of the suspect's car and detained Moore.

According to the Gwinnett County Sheriff's jail records, Moore was booked on two counts of aggravated assault, one count of felony criminal damage to property in the second degree, and one count of felony possession of a firearm or knife during the commission.

He's also being charged with two misdemeanor counts of cruelty to children in the third degree. His bond has been set at $21,700.