Animation question: Tug of War animation tip needed

I have a client within the organization that wants a sort of struggling graphic above two columns. Someone is pushing from each side, so this should look similar to a game of tug of war. Unfortunately, it can't just use a fluid motion to constantly shove back and forth... it has to move when the first column is being discussed, and then move again when the second column is discussed. When all is done being discussed, it rests in the middle of the columns.

In my head, it seems as though I have to have 3 duplicate images and use trial and error to place them in their correct resting place after the initial move, before using the animate on a line tool to move them to their next/final destinations. Is there a simpler way to do a tug of war? It really is going to move to the left, then to the right, then return to its initial position.