The sibling rivalry between Angelina Jolie and Brad Pitt's four kids is brutal, Star reports

Maddox, 6, is constantly pushing Pax, 4, around in an attempt to show him who's boss, says a source. "But Pax is no wimp, and he fights back."

But it's little Zahara, 3, who really rules the roost! "She screams and shouts at the boys when she doesn't get her way," says the source. Not even Shiloh, 22 months, is safe — and the toddler has the battle scars to prove it. "Z is always pushing or scratching her."

Zahara's picking on Shiloh is usually motivated by snacks. "Z once clawed Shiloh's cheek after she tried to take her cookie," says an insider who witnessed one incident. "She's always pulling on Shiloh's hair so she can steal her food."

"Angie gets worried when Shi plays with them," says the insider. "She always comes back with a scraped knee or a fat lip!"

"They eat fast food, pizza, chips and sugary soft drinks," says the source. "Brad and Angie let them eat what they want because it brings harmony to the chaotic household." To make matters worse, the insider adds, "because bedtime is whenever the kids feel like it, they get overly tired and cranky. Brad and Angelina don't like to be too strict."