You need to use vertex parenting- to vertex parent an object, the parent must be a mesh- now select the objects as you would to parent them normally, but then hit tab to go into edit mode for the parent, select one vertex (it should be at the parent objects center for it to work right, I’ve run into glitches otherwise) and then hit ctrl-p while still in edit mode. The children will now follow position but not rotation. If you make an object that’s just one vertex as teh vertex parent of each car (enable drawing of axes so you can see it in the 3d view as if it were an empty), and then normal parent each vertex parent to the attachment points on the wheel, it should work like you want it to.
…that description got a bit convoluted, I hope it made sense…