Play the game until completing 68% of the "Die Hard With A Vengeance" section that features the rain effect.

Immediately turn in a circle when you are able to drive.

A police car should pass by. Follow it.

If the police car disappears from view, use the blue arrows on your indicator to follow its turns. Eventually, a parking lot containing an extra life and a time bonus will appear. The baby stroller is also located in this parking lot.

Use the normal procedure to change vehicles to drive the stroller.