Here are my thoughts and suggestions.
a) Hard wired the computer to modem/router for more reliable upload must be done at all times.
b) Creating an isolated mix specific for the stream is very important. You must make sure to mic everything and send everything to the stream at all times no matter what audio mix you are sending to the local venue.
c) By passing the ATEM Mini Mic Input is not recommended and using an audio interface is extra money spent for no reason. The ideal situation is for all the audio and video processing to be done within the ATEM Mini. This will allow you to have more control over all of your video and audio settings within the ATEM software.
Make sure you have the proper cabling coming from your audio mixer (dual 1/4inch or dual XLR to 1/8inch cable as an example) that has the specific for the stream mix that you have already setup and connect that directly to the ATEM Mini. Also, make sure to use the ATEM software to have the mic input turned into line input depending on your mixer output and save that setting to the saved state within the ATEM.
Unfortunately if you have the ATEM Mini and not the ATEM Mini Pro, then you will have to add the additional issues and complexity of the computer failing or causing extra problems using your software of choice to send to YouTube. The ATEM Mini Pro can broadcast directly to YouTube with no need of a computer.
This setup has worked for many church installations that our dealers have done across Canada.
Good luck to you in solving your issues.