Grandson
The grandson may be a reference to Seuss himself. Seuss states that he "wanted people to think" about their stance or whether they disagreed with the fighting at all. The grandson is merely a listener of the story and does not take any sides, much like Seuss himself.
The Wall
The wall is a physical metaphor for the stark divide between the West and East. Despite the fact that the two are equally as impressive with their military efforts and way of strategizing, ultimately the two are enemies and cannot come together by the end of the story - much like the USA and Russia even in the present day.
Butter bread
The butter bread is a metaphor for the different political views held by the USSR and USA. One the one side, the USA strongly believes in capitalism. On the other side, the USSR is a firm communist state. This is the major source of conflicted, which is appropriately changed to a metaphor for preference of which side the butter is on the bread, for its young audience.
Inventing new weapons
The slingshots, “triple sling-jigger” and other weapons such as the “Kick-a-Poo Kid” are a funny children’s metaphor for the arms race. These comical weapons are used as a metaphor to describe the efforts of each nation to outdo the other and establish themselves as the ultimate superpower.