Possible you might not even get on your flight without it depending on where it is going . Regulations regarding these things have nothing to do with the cruise line but do involve state laws , immigration laws ( not only ours but the countries you are visitng).
I have even heard stories of problems when both parents were actually present, but , for whatever reason the names on the documents were different than the childs( ie unmarried parents). Why bother with the hassles( except of course that getting the letter from the ex is a hassle but, that's what lawyers are for).
Hope it all works out.