Thanks for the quick reply.
My initial approach to the problem was using IK (and CCDIK) but it led nowhere.
This approach has looked more promising so far, and the thought behind to get the point-to-rotate-to in relation to the rotation point and, from what I understand, using the quaternion, setting the origin axes as the parent axes to figure out the resulting rotation.
From my previous attempts and research this attempt is closer to what you suggest but, still does not seem suitable for this case.