Does Dreamhost allow you to host a live streaming webcam on your site? And if so, do they frown upon it?
I recommend that you contact DH rep and find out a definite answer from them. But I think you may get a no for an answer. As I had read somewheres on this site that uploading streaming is not aloud. However, you may convince them if your frame rate is low enough, video size is low enough, or you decide to display stills every so often. In this case though, DH does not want programs that run in the background or are a daemon. So the browser would have to request the next still.
Your other options are to switch to a dedicated server or run your own server.
But I could be wrong, which is why I said it is best to get the answer from them.