When install the trim you start with the top piece, making sure there's the same exposure on both ends and the middle. Then you start on the sides by placing a nail from the top and on the side, making sure the nails long enough to go through both pieces. I then install two nails about 6" apart on the face into the jam. With it held firmly in place and the joint tight I can now move the long part around to get my exposures right. I nail the middle, then the bottom, then go back and make sure it's tight to the jam. If not just add more nails.
If your trying to do this nailing by hand concider buying, borrowing, renting a pneumatic finish nailer (not a brad nailer). It will be worth it's weight in gold.
If your trying to cut the trim with a cheap plastic mitre box, it's never going to come out right. A compound mitre saw will be far more accurite.
It's hard for me to believe the corners are so far out of square that my suggestions will not work but if they are this simle tool will tell you exactly what angle to cut it.
Most mobile homes I've worked on had partical board for a sub floor. Not sutable for tile.
It needs to come out and be replace with something like 3/4" Advantec T&G that gets constrution adhesive on the tops of the joist and the subflooring gets screw down with 2-1/4 ceramic coated decking screws.
Then you need a layer of thin set to bed the 1/2" tile board in. The tile board gets screwed down with tile board screws, making sure not to screw into the floor joist. (a simple piece of blue tape on the walls can mark where the joist are.
The reason you do not screw into the floor joist with the tile board is your trying to pull it down where there is a tiny gap between the floor joist.