Do I understand it correctly, that when you run a scene from the editor, you want the translation in the running game to be reflected in the scene in the editor?
What you see in the editor is like a "default value" for how things are, if a running game changed that, you would never have a deterministicly running game.
Also godot can't run you game in-editor, if that's what you mean.
The remote scene tree is the state of the currently running game (spawned by godot in a separate window, that is why it's called remote - not related to the current window (editor), but the running game window). It updates as updates happen in your game while it's running.
The scene tree is the state of the scene as you want it to be when you load it into a game.