I copied over the statements I made from the Remote Force discussion to the Remote Displacement discussion because the same thing is done to create the APDL code that the solver runs.
I keep on mentioning small deflection analysis because that is a limitation on these two elements that is mentioned in their respective Help pages. This means these elements are only valid for small rotations because the equations built into the elements have used the simplifying assumption that cosine(theta) = 1. If the structure deforms enough so that this is no longer a good approximation, the accuracy of the solution will begin to degrade.
If you have large rotations in your structure, you would not use these elements. Other elements work for large deflection. I don't know if Mechanical automatically changes from one kind of element to another when Large Deflection is turned on and a Remote Force or Remote Displacement is used in the model. I would like to think they do, but I haven't checked. You could check yourself by writing out the Input file for Large Deflection ON then again for OFF and see if there is a difference in the input files.