Need to remove a remote network off of software
Putting it on your home computer will not disconnect the one at church. Each machine has to be registered individually with and email address and password but that will not disconnect another machine.
If you're talking about your WiFi network, once you're out of range of that network, it will disconnect automatically. It shouldn't affect you being able to connect to the church network.
If the remote on your phone app won't see the EW server on the church computer, make sure you follow the steps to set it up correctly on that computer. It doesn't have to be removed from one computer in the remote app to work on another computer, you would just need to go to the settings in the remote app to choose the correct server.