What if I have inserters on either side of the car, such that one is loading into the trunks and one is pulling out of them? Does it matter which is closer to the belt?

With a moving line of cars on a transport belt, a spidertron leg can cause the line to stop. This creates a gap in the line, and any inserters attempting to place items into the moving cars will no longer recognize them as inventories, and will only place items onto the belt from that point onwards ...