It's kind of sad (for me) that I never have picked up the keys, considering I've been making music for 20+ years. I can play the guitar and bass, and I know enough music theory. I know where the notes, chords, and scales lay on the keyboard, but anything else than simple melodies or chords just confuses me. My hands don't just work independently that way.
One exercise that I know people who've had success with is to be focusing on simpler scales, which will all have slightly different fingerings for both hands. Just the regular primarily white-key scales.
E.g. C major goes 12312345 for the right hand, and 54321321 for the left hand.
Then once that's doable at some speed, moving onto the tricker simple scales. And then going into contrary motion (where the right hand goes up and the left hand down). I've found that helps people get more used to their hands working independently. Especially because it provides more structure, and just one thing (different fingering) to focus on, rather than adding in differences in tempo etc.