Your door is the perfect candidate for edge constraints. Select some edge you want to be horizontal or vertical then press ALT-T or ALT-V, the re-optimize the island (press 'O' over the island).
You can alternatively use the real time optimize engine (see the panel on the right). Select some vertexes, pin them, then move them, you will see your door deforming according to your mouse displacement until you find the geometry you like.
Same orientation from 3D space to UV space? Difficult to define that thing. For many geometry this has no sense, excepted for thin and flat islands. You can have a look in Panel->Packing Properties->Initial Orientation->X or Y or Z. It change the way the packing algorithm orient your islands.