Hey there!
There's a couple of ways we can solve the problem - either by using Apache or NGINX with virtual hosts, or by creating a custom load balancer that redirects to the appropriate site (my favorite).
Running media files through a proxy is usually a bad idea, because it can interfere with things like fast-forward and seeking in the video - I can explain it in closer detail if you want.
I hope you'll get in touch, then we'll discuss the best solution for you.
Best regards,
Sebastiaan