Is it easier to apply angular momentum to a rocket with the engine off?

Question

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.

Answer 1

The chance in angular momentum is given by:$$\frac{dL}{dt}=\tau,\tau=\hat{r}\times F$$ In an ideal rocket, the main engine does not apply torque to the system, since the thrust is parallel to the position vector from which it acts (here it'll be the distance from the CoM). So we simply have $$\tau _{tot}=\tau_{thrusters}$$ so it wouldn't matter when we use these thrusters. In real missiles, there are two main problems (that I'm aware of) with this method. First, it'll be much more complicated to determine the equations of motion. Second, if we are not in a vacuum, the drag force is much bigger when the velocity vector is not in the same direction as the 'top' of the missile. You can read about "angle of attack" for further understanding, but basically if we want to turn while using the engine (and we do), we have to do it quite slowly, or else the pressure on the missile will make it fall apart.