A small item for your consideration and experimentation.
On a drumming forum, a user was complaining that practicing paradiddles didn't seem to improve his hand independence— he was working on some Chapin Advanced Techniques patterns, and was hoping the paradiddles would improve his facility with that. The answers given were all over the map, and largely based on misconceptions stemming from the use of the word independence. Aided, I think, by the notational convention of writing drum patterns as separate rhythms, as if they're played by multiple performers.
My answer was, sure paradiddles are independent, you're doing two totally different rhythms with each hand; the right hand plays 1 &a e and the left hand plays e 2 &a. You may say psha those are just backward versions of each other... and I arrogantly retort: that means you're playing the same rhythm forward and backward at the same time! Sounds pretty independent to me.
Like, look, independence:
In fact, independence = you playing one thing.
Whatever people's theories about how independence works, we're dealing with one controller— you— playing one rhythm— that of all the parts combined— using sequences of Rs, Ls, and both hands in unison. That's 100% of what hand independence is. What else is it?
If paradiddles aren't independent-seeming enough, add some unisons— play the following patterns with your right hand on the hihat, left hand on the snare. B = both hands at the same time.
Those are all at least as hard as the patterns in Chapin, and they sound independent, but done this way, they're easy to execute. So what's the difference? Mainly, they're non-mysterious, and there is no misguiding notation or language tricking you into thinking about it, and doing, it the hardest way possible.
I'm interested in other things right now, but this may be a productive way of practicing for someone: Go through the first pages of stick control and play each note of the patterns as Bs. People who have their flam rudiments together may find it easier to think of the both-hands notes as flams.
I suggest starting with:
RLLR LLRL LRLL RLRL
RLRR will be very helpful with those Chapin exercises— try replacing two and three Rs with Bs, and you'll have most of those patterns covered.
At the very least, a little bit of this kind of practice should be good conditioning for other systems of
independence coordination, and for completely resetting your approach to this topic.