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The employer should file the amendment just before you move to the new location. You can begin working at the new location as soon as USCIS receives the amendment (use tracking to know when they receive it). You do not have to wait for the amendment to be approved to begin working, though if you do Premium Processing, it isn't a bad idea to wait for approval just to be on the safe side. If you begin working at the new location and the amendment is denied, you would have to go back to the original location to work immediately.
As far as your spouse, no need to get stamped again.
And yes, filing an amendment is like filing a whole new H-1B and pretty much everything should be done again.
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