I have a construction plane at 45deg to one of the principle axes. I can align an object on the plane OK, but when I need to adjust it’s position it will only move along the principle axes, which somewhat defeats the point of having a construction plane. I’ve attached a short video showing the problem (or unwanted feature). Any solution?
By the way, TinkerCAD does it properly!
Just drag the center of the gizmo on the plane.
Thanks. I tried that and only the dot and the arrows move, not the object (it’s a single object as I’ve unioned the pieces as it wouldn’t align with the plane as a composite body). Unfortunately I can’t find an example of moving relative to the selected plane. Do you have one?
The center of the gizmo moves the gizmo, and aligns it to the object that you drag it onto. If you drag it on the plane, the gizmo will be aligned to the plane. Then you can use the arrows to move the selected object(s).
Thanks. I’ve managed it but must say that it’s not intuitive! If one has selected a construction plane then I would assume that would be used by default rather than have to wiggle the centre dot first. But I do appreciate you help - if I had longer hair, I would be pulling it out. 
@Istvan if I move the gizmo so I can drag it along a plane, but then type in a distance to translate it by, is that the distance along the principle axis, or the distance along the plane? If not the latter, how do I precisely translate along that plane using the keyboard? Or do I have to do the trigonometry myself?