Rerelease/Redispatch is a completely different concept having to do with "restarting" a flight once enroute.
If you're talking about an amendment to the original dispatch or release then as I've said before, I can't find a requirement to provide a departure alternate to a flight which has already released and encountered weather below landing minimums prior to departure. I've searched through the FARs and through FSIMS with no results. I am beginning to suspect that it is, in fact, a "creation" of sim/line operations, which is not legally required.