It sounds like you need to set up a livestream. To do that you'll need to output your composition to both your projector and an H.264 encoder by creating two screens with identical slices) to send to the web using Livestream, Youtube Broadcast or any service you feel comfortable using.
Assuming you've got enough video outputs and some funds you can invest, a quick way to do it could output your web signal straight from Resolume using HDMI and broadcast using something like the Livestream Broadcaster:
https://new.livestream.com/broadcaster.