Can you put it back quickly before the mom forgets about it and builds another nest?
I would not move it unless I could move it a few feet at a time maintaining about the same environment (amount of shade) each time. Wait a few days and observe that mom has settled onto the nest again between each move.
Tornado victims: Do not rush to rebuild. Take your time and look for and get a good contractor. Or consider selling the property and moving to a home that is ready to live in.