A couple of suggestions:
Set up port forwarding from your RPi to the Duet 2 and use that (via port 80)
Run Chromium or any other browser on the Pi directly and connect via VNC to your Pi to control the Duet
If you want to host DWC directly on the Pi, that will be a bit more complicated (unless you upgrade to a Duet 3). I figure it would be still possible either by running 'npm run serve' on the Pi (which will take a while) or by installing an HTTP server like nginx or Apache on it, but then you would still have to set up forwarding to the Duet 2.