So, the Sony 55" televisions are 48 3/8" wide. That's something to keep in mind that in almost any larger family room like yours, the TV size really should be maximized. It's almost impossible to explain how there is no such thing as too big of a TV for most homes. At a 12' viewing distance, a 85" to 100" diagonal television would be a very comfortable size, and is still too far away to resolve 4K resolution on such a display.
So, I would go ahead and triple check the measurements and see if you can fit a 55" into the space.
With a $1,000 budget, that's going to get you into the better displays available. The Sony 900f series may be one of the best looking on the market for the money and is very bright with near top shelf quality for a LCD display.
LG does have their OLED displays, which do look better, that are 48.3" wide, but the cost on them looks to be out of budget, and their brightness may not be ideal for daytime use.