Moving Animated Objects

Hi there! I am quiet new to Blender and tried creating a small animation for a piece of furniture i have in my room. It is a table, which you can rotate twice, so that the surface doubles. I have succesfully created said principle in a blender animation, but now i wonder, how to move the whole thing. If i just select everything and move it, the Animation get´s screwed up because of the keyframes. If i create an empty as a parent for everything, the same happens. Even delta transform still screws up the animation!
The animation works with 2 rotation axis (represented by the arrows) which i defined as the parents of the table-covers with constrains. The lower cover, only has to rotate once, so it`s parent stays the vertical arrow, but the upper cover has to rotate twice around different axis, so i change it´s parent on frame 10 to the second axis.

I hope you have some tips on how to fix this. Also, as a new user on this forum, i share files.

That is because the only object you should parent to the empty is the parent of your table. If you try to parent all objects you will destroy the first parent relation you had between the table parts.

So basically, only the parent should be parented.