Given that the legs move a little bit, I would suggest adding at least a small amount of bracing in addition to whatever you choose to do to fix the center of gravity problem.

Also, bracing helps to stiffen the structure by resisting forces that would make the wooden rectangle into a parallelogram. Here is an illustration:

Even if you feel that the white house should stop being used as an active part of the USA government, it doesn’t make sense to tear it down.

Take Auschwitz for example - a horrible place, but worth preserving so that future generations can see history in person and learn from the past. At the very least, the whitehouse is worth preserving for its historical value, if nothing else.