When you're considering the television, keep in mind to not place it opposite a window. The reflection will cause you to have to close the drapes when watching.
My daughter has a set up like this (one long room). Since your doors are in the "living" area and are drafty, I suggest you make this area for dining, and the dining space for the tv and sofa/chairs. I think the area to the left of the door will be a fine size for a small table and chairs (perhaps even a craigslist cabinet as I'm sure your mom has some treasures and mementos she would like to display.
The sofa would then work on the long wall in the (former) dining space and the tv could then be next to the bedroom door and shouldn't be affected by any reflection.
Anyway I would try this arrangement before committing to purchasing anything...
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