A receiver is just a fancy name for Stereo. Many inputs and outputs, connect to speakers for sound.
OK. Here are your options.
SIMPLEST SOLUTION - just buy a sound bar for the TV room. Immediate impact on the sound quality in the TV Room for TV, Blu-ray, TiVo streaming, etc. There are many options from $200-$700, the sweetspot for just sound being around $400. The increase in price can lead to thinner design, more channels for audio, and added subwoofers. Samsungs wireless solution for your TV with wireless subwoofer is $500
NEXT STEP UP - invest in a wireless sound bar for the TV Room to build a system for the future. SONOS, Bose, LG, etc. all have this option at $500-$700. This would allow you to have all the benefits of the simple solution, and provide options for the future.
THE ALL IN SOLUTION - What options? This all in solution. Wireless soundbar for the TV room ($500-$700), add a SONOS Connect like device to your stereo in the parlor room ($350). This would give you all the advantages of the simple solution AND allow you to stream your Parlor room music to the TV Room and vice versa. You could then add wireless, movable speakers to your system for flexibility.