How much are you willing to sacrifice your living room space for the benefit of your recording setup?
Keeping in mind that left-right symmetry is critical, it seems to me that having your desk facing the patio doors is probably your best location in that room. Depending on the size of the desk, you may still have room to open the bedroom door. You may also find that your best position in the room is away from the patio doors far enough that you can walk around the desk to access the patio.
Once your position is established, then you can tackle acoustic treatment locations (first reflections points and LOTS of corner traps as a starting point). Having some movable (stand-mounted) panels, and your desk on wheels, might be a good option that will allow you to set up the space for recording/mixing, and then move it out of the way for living.