If I go with this beam model, I would have all rotations released on both ends...
I don't really see a reason to release both end, but if you do make sure you have rigid mode search on for the modal analysis; the beam will undergo rigid body rotation.
In this situation, the points in question would always overlap when projected vertically. The more I explore, the less I think this is possible.
Let me preference this by saying that I could be misinterpreting what you're trying to do. With that out of the way, I think you've defined a contradictory condition. You cannot have two points that have a unit vector between them remain constant while also allowing rotations to exist at either point, especially when these points are part of a deformable surface.