Police say 24-year-old Francisco Miguel was pulled over Sunday morning for driving erratically while eastbound, near Exit 57, at approximately 2:30 a.m.
Miguel was charged with felony driving while intoxicated under Leandra's Law for operating with his son and niece in the vehicle.
The infant's mom, 18-year-old Sonia Diego, was also in the car.
Both Miguel and Diego were charged with endangering the welfare of a child.
Miguel was held on $2,500 bail and remains in Suffolk County Jail. Both are due back in court on Aug. 13.
The children were released to a relative.