The 23-year-old woman was driving her grey Toyota Yaris along Harehills Road when a man stepped out into the road causing the woman to brake suddenly.
He confronted her but she continued driving.
However, as she stopped at the traffic lights further up the road near to the junction with Ashton View, a black Ford Fiesta bumped the rear of her car.
Then a man, who had his face covered, got out and smashed her rear window with a hammer.
He is thought to be the same man from the earlier incident.
The expecting mother managed to drive off and phone the police.
The suspect has been described as white, aged 23 to 24, with short dark brown hair.
He was wearing a grey jumper and blue jeans.
The Fiesta was believed to have had a registration ending AXC or similar.
The incident, which happened between 3pm and 3.30pm on Monday, May 6 has sparked a police appeal for information.
Officers are keen to hear from anyone who witnessed the incident, particularly if they were driving in the area and have any relevant dashcam footage.
Anyone with any information that could assist the investigation in asked to contact PC 0906 Sogbetun quoting crime reference 13190231424.