If any of the DMD's halted the disease progression completely I'd take it....side effects and all! But that's not a realistic idea. I can't imagine a Neuro expecting that or even voicing that opinion. If a DMD completely halted the progression then I'd call it a cure.....or as close to a cure as we'd find.
I wouldn't let this particular Neuro force me into anything I wasn't comfortable with. The interferons have serious side effects. If he's happy with Copaxone I'd stick with it (no pun intended!

). I can't see that anything you've reported makes Copaxone a failure in this instance.
Others will be along with their opinions. You'll find lots of support and good advice here.