Your soundbar has three inputs. You can use a different input for each source. How you do that will depend on what connections you have on the TV and DVD. You could use optical for the TV and HDMI for the DVD. If you want to use the aux input then an audio input selector is what you would use rather than a Y splitter. https://www.amazon.com/Stereo-Manual-Selector-Sharing-Switch/dp/B00NTJET10
Connecting the DVD to the soundbar directly allows for CD playback without turning on the TV.
Normally the DVD player would be connected to the TV and the TV audio out will go to the soundbar. But you can use a splitter or a mixer if you want for whatever reasons.
Your soundbar has three inputs. You can use a different input for each source. How you do that will depend on what connections you have on the TV and DVD. You could use optical for the TV and HDMI for the DVD. If you want to use the aux input then an audio input selector is what you would use rather than a Y splitter. https://www.amazon.com/Stereo-Manual-Selector-Sharing-Switch/dp/B00NTJET10
Connecting the DVD to the soundbar directly allows for CD playback without turning on the TV.