If by current camera, you mean the iPad, then look into the free Larix Broadcaster app (https://geo.itunes.apple.com/us/app/lar ... 74385?mt=8
). This app will send the camera feed via RTMP/RTMPS to whatever server you list. Get a persistent stream key for Facebook and enter the details in the app. Or setup a RTMP server on the Pi if you're trying to mix in sound from the board, then forward that to Facebook. Then all they have to do on Sunday morning is press the start button on the iPad, and control the stream from any web browser.
The only concern in that setup is how to get the sound from the mixer into the Pi, since it doesn't have native audio input... I guess you would need a sound HAT? Here's a list of options for that: https://www.tech-knowhow.com/2017/06/ra ... tive-list/
For what it's worth, when properly done, the OBS Studio route can be really easy. I bought this keypad
and labeled it for all my scenes and overlays (even set a few Windows macros to start everything needed on the computer), so that the only setup needed on Sunday would be setting up and turning on the cameras (phones), then pressing start on the keypad. As far as the camera phones are concerned, I'm working on setting up the RPi's I have to become NDI cameras, so that all that would need to be done is point them where they need to see and plug in power. When I finish setting this up, Grandma should be able to operate it.