Amal Khalaf, 41, told jurors through an interpreter that she screamed "No! No! No! No!" at Faleh Almaleki and held up her hands before the two women were hit in October 2009.
Almaleki's 20-year-old daughter, Noor Almaleki, died 13 days later. Khalaf suffered a broken hip and thigh and spent about two months in the hospital.
Authorities accuse Almaleki, 50, of intentionally targeting his daughter because she had brought the family dishonor by becoming too Westernized. He has pleaded not guilty to charges of first-degree murder, attempted murder, aggravated assault and leaving the scene of an accident.
His lawyer said during opening statements that the truck driver from southern Iraq was angry at the older woman, who is the mother of Noor's boyfriend, and was trying to drive by and spit on her when she jumped in front of his Jeep.
He swerved, but could not avoid accidentally hitting her and running over his daughter, his lawyer said. He fled after the accident, making his way to Mexico and then to London, where he was detained by customs officials and returned to the U.S.
Prosecutors say he did not flee because he panicked, but because he wanted to avoid capture.
Khalaf left her native Iraq with her children in 1994 and came to the U.S. in 1997, when she said she first met Almaleki, his wife and their children in Michigan. Her family moved to Phoenix, and the Almalekis followed in 2004.
Faleh Almaleki, who is from a small southern Iraqi town near Basra, and his family were relocated by the U.S. military to Saudi Arabia and then the U.S. in the mid-1990s.
As Noor Almaleki entered her late teens, she became more and more estranged from her family, prosecutor Laura Rechart told jurors in her opening statement last week.
Faleh Almaleki wanted Noor to act like a traditional Iraqi woman. But at 17, she refused to stay in an arranged marriage, angering her father. He also wanted her to remain at home and take care of the younger children while the parents worked, the prosecutor said.
She moved into her own apartment at 19 and began working at a fast-food restaurant, but quit after her parents kept showing up at her work, insisting she return home, according to court documents. Later in 2009, she moved in with her boyfriend, Khalaf and Khalaf's husband Reikan, after saying her parents had hit her.
Khalaf had taken Noor in several times after she left home between 2007 and 2009, and that was a cause of increasing friction between the families, she testified. Once while Noor was staying with the family, police were called after Almaleki and his wife showed up at their home.
Noor moved in again about seven months before the incident on Oct. 20, 2009, outside a state Department of Economic Security office in the west Phoenix suburb of Peoria. She said Noor had gone with her to interpret and the women were waiting to be helped when Faleh Almaleki came into the office.
He left after a short time, and Khalaf said she was worried he might do something violent toward Noor, so she drove around the parking lot to make sure he had left. She testified that she was so nervous, she locked her keys in her van and had to call her son to bring another set.
They left the office to go to a nearby restaurant when the Jeep bore down on the women, she said.
"I thought he was not going to hit me, but I was protecting her," Khalaf said. She described Faleh Almaleki as looking angry as she screamed at him to stop.
A detective testified earlier that Almaleki acknowledged under questioning by police that he intentionally ran over his daughter. But the transcript of the taped interview showed he repeatedly called the incident an accident.
Prosecutors were expected to call Reikan Khalaf and other police officers to testify next week.