Chickens are creatures of habit -- they often pick their favorite nest and stick to it!
The best thing to do when moving a broody (in my experience) is to contain her somehow so that she can't go back to her original nest. But, of course, she still needs a space outside of the nest so that when she gets off she can get food and water and poop.
What I use for my broodies is a large rabbit hutch that's divided into two sections -- an "indoor" section that is walled in and dark (essentially a nesting area) and an "outdoor" section with screen walls where the food and water are.
I know that not everyone has access to this ideal setup. As a last resort, when the chicks are pipping (as yours are), you could move her to the new nest box and simply close her in until all the chicks hatch. Since most hens don't leave the nest while their chicks are hatching anyhow, having no food/water/poop breaks for 24 hours probably won't hurt her too much. Make sure it's dark and comfortable, but also make sure they have adequate ventilation.
I move my broodies and eggs late at night when it's pitch dark. Then she can't see enough to be upset that she's not on her favorite nest, and when she wakes up on the new nest she's already spent some time there and may decide it's OK.
Moving broodies is always a risky business as you can never really predict what will happen. Whatever you do, make sure to keep a close eye on her.
