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The brawl was captured on Snapchat and shared on Facebook more than 2,000 times.
The video shows parents throwing punches after one witness said another parent cursed at a child that wasn't his.
Police said seven to nine people were involved in the fight; four were arrested.
Gary Gatlin, Geremiah Gatlin, Audrey Gatlin, along with Latrell McDougald were arrested and charged with simple assault.
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According to the arrest reports, the four used their hands, feet, and teeth in the fight that injured one person.
"We do encourage everybody that if you are involved in some type of verbal altercation or even if you're a bystander and you see something like that, call 911 so we can get officers there before it turns physical," said Sgt. Sean Strepay.
Robin Skipper was at Chuck E. Cheese's on Sunday for her nephew's birthday party. She said it was absolute chaos.
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"I think it's a shame you can't take kids anywhere without adults acting like that," said Skipper. "It was bad; there were kids screaming. I was worried about my kids getting trampled by the fight."
The police department is still looking for additional suspects in the fight.
Those with any information are asked to call Crimestoppers at (910) 483-8477.