I definitely recommend avoiding Turkish Get Ups for now because there are a lot of prerequisites you'll need, and the variations in movement are more complex, so there's a greater likelihood of doing more harm than good. You'll want to start with isometric core exercises, then progress from there. That anti-rotation cable push out is a good place to start. It's easy to check your technique because if you draw an imaginary line bisecting the body, both sides should look symmetrical, so you'll be able to correct compensation patterns more easily.