Sorry to hear that's happening. If you're seeing a persistent crash, I would recommend rolling back to an earlier save before the issue takes place. You might also try clearing the Xbox Cache (to remove title updates) and deleting/re-installing Dawnguard.
I too have the same issue, Xbox Slim, 70 gig free on HD, Skyrim on HD, DG on HD, worked fine until I got DG, now every game it freezes up and loading screens that used to take maybe up to 20-30 seconds to load, now can take 4-5 minutes, or just lock up totally, DG needs to be fixed .....
Reinstalled 3 times now, everything, even does it with new characters, no dice, its only since DG though before it would freeze maybe once every 100 hours plus, now its every 2 hours if I am lucky .........