Answering this question will require you to analyze your own cognitive process and compare it to the cognitive process used by skilled musicians. Right away, we have a problem: There's no way to get an objective view of your own cognitive processes, let alone of those of others.
- How do you know whether you are doing (1) or (2)? What would be the test? What if you can do (2) for certain polyrhythms but can only do (1) for others?
- How do you know whether a skilled musician is doing (1) or (2)? Some professional drummers might claim they can do (2), but there's no way to verify this.
That said, from the way you've framed your question, it's obvious that true independence (2) is a more powerful skillset, and (1) is a subskillset of (2) or a stepping stone on the way there. But I will be brave and say that you shouldn't worry about this.
True independence is rare
For the reasons given above, I can't prove it, but I doubt that many musicians are ever able to achieve true rhythmic independence. The exercises used to teach young pianists to play 2 on 3 or 3 on 4 all center instead around developing a "gestalt" that combines the two rhythms, such as the saying "Nice cup of tea" for 2 over 3. This is precisely what you are describing in (1).
Even highly skilled musicians, when playing polyrhythms, will usually alternate between thinking of one rhythm as the base meter and the other as an embellishment. Sort of like the spinning dancer illusion, we can alternate between bringing the 3 or 4 into "focus", but it's virtually impossible to give them equal cognitive weight.
Functional independence
Instead of trying to develop true independence, the polyrhythm exercises I did in music school focused on memorizing the gestalt patterns and then training yourself to swap the primary and secondary rhythms as quickly as possible. This is the approach jazz drummer Ari Hoenig takes in his polyrhythm videos. Let's call the ability to alternate quickly between assigning focus to one rhythm or another functional independence, since if you can do that, you can function in basically any musical context.
A starter exercise is to tap your favorite polyrhythm (2 on 3 is a good place to begin) while feeling the left hand as the primary beat and the RH as the second beat (permutation 1A). Then, switch the part that each hand is playing without breaking the flow (permutation 2A). Now your right hand has the primary beat. Now, silence the right hand and allow yourself to acclimate to the left hand as the primary beat. Try reintroducing the right hand at the same pace but while continuing to feel the left hand as the primary beat (permutation 2B). Then, switch the parts that the hands are playing once more (permutation 1B). Now you have cycled through all possible permutations.
Here 1 and 2 refer to the configuration of the hands, and the letter denotes which rhythm was given precedence. To an outside observer [1A and 1B] and [2A and 2B] look and sound the same, but the difference is in how you are internally feeling the beat.
You can come up with ways to extend this using a metronome or drum track as the primary or secondary beat.
