Since the tone of the piece is light-hearted and the main characters are 6 and 13, I would say it sounds like middle grade (despite the Cuban Missile Crisis reference and the '60s time period).
I think it really comes down to the simplicity (or not) of the plot. If you go for the adult market, the plot would need to be complex enough to keep their interest.
As for middle grade short stories, I believe there are pubs that accept that kind of story. I'm new here, but I think there are resources on this site that can point you in the right direction there.
Good luck!