In this video tutorial, I show how to rigorously solve the so-called "Triplet Paradox", first in the simplified case of instantaneous turnaround, then in the realistic situation where a finite acceleration is taken into account: https://youtu.be/Dy8fC2eVOeA
"Every round trip, no matter how it is physically constructed, involves rotational motion"
WRONG!
Had you actually watched the video tutorial, you would have seen that it considers a rocket with dual thrusters (in the front and in the back), so no rotation is required to come back.
Also, even if a flip maneuver is performed (such as the flip maneuver that SpaceX is capable of doing), the relativistic effects associated to it would be ridiculously small compared to the relativistic effects due to the speed.
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