I don't see your problem. "die Feuerwehr" means "fire brigade [in general sense, not related to a fire brigade within a company]", "firework" means "[das]Feuerwerk". A child can see both.
isn't firehouse the same thing as fire department?
A firehouse is the actual building where the fire trucks are kept. The fire department refers to the whole entity as a public service, with the firemen included.
can't it be "that kid"?
"The child is seeing the fire department. " Is it wrong?