Hi Cal, To get the camera inputs into EW, you would have to have them connected to the computer via a capture card or through NDI out from vMix and create a feed in EW under the Media tab > Feeds. If you already have them connected to the other PC, you wouldn't be able to have them display through EW at the same time.
However, if you do have them set up in EW as feeds, you can use those feeds as your backgrounds for your songs and scriptures.
You could feed your cameras into HDMI splitters and the feed one output to EW and one to vMIx. You could then use the inputs seperately in each program.
There are ways though to do it vie NDI using the NDI Tools.
I am a little confused as to exactly what you are wanting to do. You say you have an ATEM Mini but want to use EW6 with vMix.
If you have vMix, why would you want to use the Atem?
I assume you have a PC running EW 6. Are you wanting to feed the two cameras into the ATEM then to EW or are you planning to feed vMix into EW as a feed? Assuming too that you cameras are all HDMI.
Either way you will need and an HDMI capture device to capture the output of either the ATEM or vMix. I assume your Elgato is working fine.
Depending on exactly what you want to do will depend on how you need to set it all up
I agree with Alvin. Toyin, we need more info on what you are trying to accomplish.