As she was attempting to turn around, police descended on the vehicle and smashed the windows, pulling her and her nephew from the car, Mr Mincey said, adding that the toddler was then pulled from the backseat.
Ms Young had to be taken to hospital for treatment, while the baby remained with police officers, Mr Mincey said.
"Her face was bloodied and she looked like she had been beaten by a bunch of people on the street," he told the Washington Post. "She is still in pain."
The toddler was left with a large bump to the head, he said, adding that mother and son were separated until the following morning.
Ms Young was released without charge. Police have failed to inform the family where the damaged vehicle is, or the belongings inside it, which included her son's hearing aids, the lawyer said.
An FOP spokeswoman told the BBC the union "immediately took the photo and caption down" after it became aware of "conflicting accounts of the circumstances under which the child came to be assisted by the officer".
Protesters have clashed with police over the death of Wallace Jr.
His family say he was suffering a mental health crisis when he was shot by officers. Police say he had refused to drop a knife.
Large protests broke out in Philadelphia earlier this year following the police killing of 46-year-old African-American man George Floyd in Minnesota. Footage showed white police officer Derek Chauvin kneeling on Floyd's neck, while he repeatedly said he was unable to breathe.
Floyd's death sparked protests around the world against racism and police brutality.