K.M.
Your dress sounds lovely for an evening wedding. Your cousin, on the other hand... absolutely not. You are correct, this is a complete no-no. She could dye the dress or have the store order the correct one.
There are so many choices out there- is this dress really 'all that' and she can't find anything else???
And yes, I agree with the other posters, the gown ladies will look out of place.
But on a positive note, have a wonderful time! Enjoy getting dressed up and having an evening out!