Automatically mix audio is the setting I need to understand how to work.

So if I'm playing a input that contains a video with sound, I disable automatically mix audio and it should remove the sound from the mixer but allow the sound from the video to be played both in our in house mixer and on the streams? Am I getting close?

Personally, I'd try to solve this by using a hardware audio mixer where you can create different (aux) output mixes, and therefore ensure that the output mix being fed to vMix doesn't include the audio from the video that's being played (whilst also generating a different output mix with everything that should be fed to the sanctuary). If your current audio mixer can't do this then you could add another very small mixer (no more than two channels are needed) to take (a) the feed from the vMix PC (so it doesn't go into the main mixer and get sent back to vMix) and (b) a feed from the main mixer, and then you can create a dedicated mix for the sanctuary.

Alternatively, if you need to feed the video playback audio into the mixer, and can't create two different mixes from it, then it's possible to let the hardware mixer create the "master" mix for vMix, and to break the feedback loop by removing the video playback audio from vMix's internal Master audio bus.

Either way, you need to create a dedicated "clean feed" output of the video playback audio to connect to an external mixer. To get that clean feed you will need another audio output device for the PC, something like the Behringer-UCA222 USB interface. Then, for the video playback input in vMix, you will change the audio routing so that it doesn't get sent to the Master audio bus (disable the 'M' button), and instead send it to an otherwise unused audio Bus (one of the A to G busses). Finally, in the vMix settings, select the new audio output device as the destination for the audio group that you've used, and now you'll have a "clean feed" signal that can go to an external mixer.

What will happen now is that the external mixer will handle all the audio mixing, including the feed of the video playback, and that mix will be sent both to vMix (with no feedback loop) and the sanctuary.

Alternatively, if you're going down the other route of using a second mixer to combine the video playback audio with the rest of the audio coming from the main mixer, you will still need to set up the "clean feed" output as above, but this time you need to keep the 'M' button on for the video playback input so that vMix adds the video playback audio into the vMix Master output mix.