Los Angeles County deputies said 55-year-old Marie Shipley was seen by witnesses near Apollo Park in Lancaster Monday afternoon.
Her three grandsons, ages 7, 11 and 13, were in the van with her.
The boys started to argue, and Shipley ordered them out of the van while it was moving. It's not clear how fast the van was going at the time.
The 7-year-old then tried to get back in, but he fell to the ground when she began to accelerate. He suffered minor injuries to his arm.
One of Shipley's daughter-in-laws, Krystal Sandford, said she can't believe the allegations.
"She's a very, very loving woman, and she takes very good care of her grandkids," said Sandford. "I don't understand what's all going on, but I really hope that she gets home to us soon."
Shipley was arrested at her Lancaster home.
Deputies said the other children involved were not hurt during the incident.