In the "big red ball" vs. "red big ball" case it can be deliberately used to change the way the term parses. The "normal" one means a ball that is both red and big. The abnormal one implies that "big ball" is lexically a single object, perhaps a proper noun, and that the "red" modifier is being applied to it.
This is the exception that proves the rule, though, as "big" is now in fact part of the ball's identity, rather than something merely describing the ball.
Seeing this phrase (or "Begs the question") used appropriately is always a pleasant surprise.
You hear an example in Boris Johnson PM talking about "new _blue_ passport", people getting a "new passport" is a thing, but if you say a 'blue "new passport"' then people will find that a foreign turn off phrase and assume you're a non-native speaker or you're having a stroke (ie a medical problem with your brain).
I mean, yeah, if it's a noun phrase it might work, but even if we're taking about a red zorb, it's not going to be "red big ball" unless Big Ball is a trade mark or brand name or whatever.
I can't imagine any editor would let you get away with something like "the red big-ball."
Let's change the noun. If a native speaker says, "big red hands," you can normally assume they're speaking of large hands which are colored red.
However, if they say "red big hands," this parses to "red big-hands," meaning "big-hands" is treated as a title, or perhaps a brand. You might see this title capitalized: "red Big-Hands".
Going back to the first example, if you mean "red hands" as a title, you could write "big Red Hands" or better yet, "big Red-Hands," meaning something big with the title Red-Hands. Since the adjective order is the same as grammatically conventional English, the hyphen helps distinguish the writer's meaning. But nowadays I find writers often leave it out when the adjective order implies the multi-word title.
hairy brown bigfoot. :-)