I have a Dot integrated into my home stereo system along with TV sound. The best way is that TV audio and Dot audio (along with all other sources for entertainment center (e.g. blu-ray, FireTV, Roku, Chromecast, media player, etc, etc, etc) each have their unique inputs, so we HAVE to switch source switch to use one or the other -- no auto-switching allowed.
Dot for my TV is ONLY for the aux out input for stereo, and not other Dot features. Dots are cheap when on sale, so get another so you can dedicate one to this audio purpose. An Echo and Google Home are across a short hall if we need to ask questions or give commands. We name our many Dots "echo" and our Echo is named Alexa. This minimizes and adds to confusion depending on how you look at it.