Hi again
First of all, consider that a relative tween sets its final endValue as "relative to its start value", but after that is done, both the startValue and the endValue are "fixed", meaning that if you restart the same tween after moving your target, it will jump to its original startValue and tween to its original endValue.
That said, you shouldn't move a Transform when working with the UI, because changing the transform's position of a UGUI object can hit performance quite a lot, since Unity has to "rearrange" a lot of variables to then keep correct anchors, raycasts, etc. You should instead change a RectTransform's
anchoredPosition, which is much more performant.
You can animate that by using the RectTransform shortcuts (specifically
DOAnchorPos). Also, if you do that, TADAH! Everything will still work correctly after your screen changes from landscape to portrait and viceversa, because while a UGUI's Transform position actually changes when the screen layout changes (and thus the "fixed in stone" relative tween will behave as I explained in the intro to this post), a RectTransform's anchoredPosition doesn't