Dave (BTW you have the same name as my nephew!), I think the best answer to this will come from Carnival. I think I'd ask for a supervisor instead of talking to a PVP (unless you have one already).
It could be that they would let your wife on with proof that she's filed for a new card, but I wouldn't count on it . Hopefully she'll get her new Greencard before you sail.
(If she lost it recently, has she retraced her steps? Could it be in the bank safe deposit box? In a purse she hasn't used recently? In a coat pocket? With her passport? If she's applied for a job recently has she checked the info she took with her? Just some suggestions! )
I hope that she either get's her card or finds the old one ASAP!
"A truly happy person is one who can enjoy the scenery on a detour."
Golden Princess 2009 Carnival Conquest 2010
Grand Princess 2010 Island Princess 2011
Grand Princess 2011 Carnival Magic 2012
Carnival Dream 2012 Island Princess 2013
Carnival Magic 2013 Carnival Legend 2014
Carnival Magic 2015 Coral Princess 2015