Bingowings said:
I'd say neither.
I'd have Anakin's sword stolen by Grievous and retrieved from him or better still from Padme's pad or ship (she could have brought it along because of the mystery of him leaving it behind and what that implies).
What you just described, with Padme bringing the lightsaber to Mustafar, is actually a very cool concept, and is pretty much the only way I'd be okay with this idea. But then again, that sounds like it'd be a nightmare to edit.