The best way to practice independence of the hands is this:
Start playing your pattern with the left hand (slowly!). With the right hand, play one fixed note on the first beat of every bar. This should be simple.
Now play quarter notes with the right hand - still stay on one note though. Practice until it is fluent. Speed it up a little until you feel comfortable with the new tempo.
Repeat and continue that exercise with various simple and later more complex rhythms with the right hand. E.g. play eighth notes, then play two eighths, a quarter break, two eighths, a quarter break. Later add playing only off-beats or even a Latin rhythm.
The key is:
- play it slowly with a simple rhythm until you feel comfortable (i.e. it runs automatically).
- Speed it up a little. Again practice until you’re comfortable.
It will take you a few weeks of daily training to be able to comfortably play independent rhythms with your right hand. But you will most likely feel the first hint of “independence” on day one :)