Using a traditional setup you can have two instances of obs open and may be able to stream separately to each service, however, your webcam would not work on one of the streams (as as far as I'm aware, can only be used by 1 streaming application at a time).
You can stream and record to a local file simultaneously using obs and then upload later, or perhaps stream the recording? (although I, and several others, have been having trouble with this:
post 1,
post 2)
Alternatively you might be able to use the RTMP server configuration that is talked about
here and also by
@Jack0r on his webpage
here. I am not sure how this would work 100%, but perhaps you could stream from pc one, send it over to PC 2 and stream the exact same stream from PC 2 on YouTube Gaming. I can't be sure though as I could never get my RTMP server to function correctly on my internet( its managed by a company, not me).
Hope this helps :)