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."