A South Shore man was charged with domestic battery after he allegedly beat his girlfriend and her son early Monday before throwing her 8-month-old daughter from a moving vehicle, which then ran the baby over in the Greater Grand Crossing neighborhood on the South Side. Joseph Fults, 46, was charged with one misdemeanor count each of battery and domestic battery, police said early Tuesday.A fight broke out between Fults and his 23-year-old girlfriend about 2:40 a.m. inside the vehicle near Cottage Grove and 75th Street, police said. While hitting his girlfriend, the woman’s 7-year-old son tried to intervene and the man proceeded to strike the boy, police said.Fults then threw the woman’s 8-month-old daughter from the window of the vehicle and, as he sped off, the vehicle ran the child over, police said.