Shifflett tried to leave the scene, but she was stopped by the daughter, according to authorities. She was arrested and taken to the Allegheny County Jail.
The mother suffered serious pelvic and lower body injuries. She was taken to a trauma center.
The daughter suffered facial injuries during the initial fight with Shifflett and was taken to a Pittsburgh hospital.
Police said Shifflett was found to be "highly intoxicated."
Shifflett is charged with attempted homicide, aggravated assault, aggravated assault by vehicle while DUI, aggravated assault by vehicle, recklessly endangering another person and DUI.