The chain reaction crash put 21-year-old Patricia Mechuca and her twin 9-month-old boys in the hospital.
They were visiting for the weekend from Baltimore to ring in the New Year with loved ones.
"One of the babies is getting better. The other one is getting worse," said Andrea Sosa, a relative.
Police 57-year-old Gregorio Patino, the driver of the livery cab was heading south on 4th Avenue at 1:15 p.m. on Sunday.
He hit a double parked mini van causing that vehicle to hit a legally parked pick-up truck which mounted the sidewalk.
The mother had her boys in their stroller waiting for their ride back to Maryland.
"He tried to swerve over," said Evan LeBron, a witness.
Mechuca, her sons, the driver and three passengers inside the livery cab were all taken to Lutheran Medical Center.
The livery cab passengers included a 40-year-old woman with a broken leg and wrist, an 8-year-old boy who suffered a broken nose, and a 16-year-old boy that suffered some facial injuries and is now in stable condition.
Police are not sure why the livery driver lost control of his cab.
Patino was arrested and charged with driving with a suspended license, reckless driving, and imprudent speed.
"They won't let me see him. They won't let his daughter see him. It's hard," said Maggie Rosato, the livery driver's niece.