Let's say I've got a rocket that I need to rotate for my next maneuver. Assuming it's flying through full vacuum, I can turn off my engine first, and then use reaction control thrusters to rotate, or I can rotate with reaction control thrusters with my engine still pushing. Intuition says that it should be easier to rotate without the engine running, but rocket science is often counterintuitive. Is there a difference between trying to apply angular momentum while the engine is off, and trying to applying angular momentum while the engine is simultaneously applying linear momentum?
*In real spaceflight, once the rocket's escaped the atmosphere, burns tend to be short and happen strictly while aimed in the desired direction. More like aiming and firing a gun, and less like turning a car while accelerating. Let's ignore that here.