Absolute orientation alignment with vectors
A simple modification of Horn's approach can be made to incorporate local rotation information: rather than just matching the centers of the body (trajectory points), use several off-centered points on the body such as the endpoints of a tied reference frame (in a way, forming dipoles, quadrupoles, octupoles...). Then use Horn's method on this augmented point set.

By adjusting the remoteness of these points from the center, you can trade good translational fitting for good rotational fitting.

This aside, you can probably develop a method based on static equilibrium of two solids (formed by the whole trajectories), where elastic forces are developed between corresponding points as a function of distance and torques as a function of misalignment.



CAUTION: in case there is significant scaling difference, you will need to adjust the remoteness proportionally to the size of the whole trajectory, otherwise artificial discrepancies will arise because of rescaling.