If the house is made in Element, make the door in Element too.
It should still be able to follow it if you make the door outside of Element though. Simply make it a 3d layer. You can use the tools in Element to create a null object at certain points on models and that will let you see where in 3d space you need to place the door layer.
It's a little hard to tell from your picture but... If you make the 2D door active in 3D space by hitting the checkbox in the 3D column (cube icon), then the door will respect the camera movement. If you don't have a camera in your comp, you'll need to add one first.
The trick is to put the door in the proper place in relation to your Element3D model. That will take some tweaking of the three posotion parameters of the door but you should be able to dial it in by moving the camera around a bit, make tweak to the position, move the camera, tweak, etc.
Hope this helps.
Without some serious knowledge, you can't put the door inside the element3d model. That would require adding the door as an element in your E3D set up (inside the plugin). It can be done but you would need at least a simple plane shape and the door image as a texture on that plane.