In Little Molly Modern's frame of reference, her mother's train travels to the left while her father's train travels to the right. Both trains happen to be the same length if they have the same proper length and if they happen to have the same speed, even if they are traveling in opposite directions. As we shall see, if they were traveling in different speeds, they would have different lengths in the direction in which they are moving.

Since each train has a proper length, we should give a proper length to Molly. Let us say that the railroad crossing to the right of Molly's school is Dixon Street and the crossing to the left of Molly is Maple Street. The distance from Maple to Dixon is Molly's proper length, and we will set it at the trains' relativistic length.

Trains moving left and right, schoolhouse stationary.

Little Molly must see the light from the lightning flash reflected from the caboose of each train as reaching her before light reflected from the locomotives. Each caboose is traveling toward the lightning flash and so the light need not travel as far as light reflected from the locomotives, which are traveling away from the source of light.

Molly sees the burn marks left on the rails by both cabooses simultaneously and then, a little time later, burn marks are left on the rails by both engines simultaneously.

First cabooses, then engines:

Now this lack of simultaneity between the caboose and engine of each train each leaving their mark on the rails will be observed by all of Molly's friends on the playground and the crossing guards standing on the ground near the ends of the trains where they leave their mark. Everyone in Molly's frame of reference, in the world of school buildings, rails, wooden ties and gravel, can agree on what is meant by "at the same time." Their clocks can be synchronized.

They may see the light at different times but that is not the celebrated time desynchronization of Einstein's relativity. What they see is desynchronization due to signal transmission delay time. That kind of desynchronization was understood long before Einstein, and they can account for it. That is the difference between observing and measuring.

So while Molly only sees both cabooses leave burn marks simultaneously because she happens to be the same distance from each of them, she would measure the same result even if the distances were different. To measure, she could compare observations using identical clocks at different locations. These identical clocks must, however, be at rest relative to each other. 

Moving clocks, however, are a different story.