Or get a bike designed for hauling.
Here is my Giant Transport. I use it every weekend in the summer to go to the track. Strap the truggy on the front rack, and the pit bag to the rear.
It's a neat bike, because the racks are hinged and can collapse. Very heavy duty. Here it is. In the second pic, it's the center bike (see how the racks can fold down over the rear tire). Pardon the pics with adult content:
