VCam and streaming are completely independent from each other. Set up both independently, do both, and watch it work.
What is NOT possible, at least not without a hack, is to stream to two network services at the same time. OBS only does one...officially.
The hack is to put the second URL into the filepath for recording, but of course you lose the ability to actually record that way.
What *might* be possible, is to install a restreamer, either on the same machine as OBS or on a different machine that has a good internet connection. ('cause it's going to have multiple simultaneous outgoing streams) A Raspberry Pi or a smartphone should be okay to run the restreamer, as it's only *copying* data, not creating it like OBS does.
Set OBS to stream to the restreamer, only, and then set up the restreamer to copy it everywhere. Here's one:
Live video streaming on your website without a streaming provider. Latest release v0.6.8
datarhei.github.io