The correct way to distinguish between coordinate and non-coordinate adjectives is:
If adjectives are coordinate, you should be able to list them in any order without changing the meaning of the sentence or creating a sentence that does not make sense.
Coordinate adjectives equally modify the noun and can be rearranged without affecting the overall meaning. In contrast, non-coordinate (or cumulative) adjectives must appear in a specific order, and changing that order may affect the meaning or create an awkward sentence.