First I have a question, if you'll all have the same last name how did Carnival know it wasn't you'll child together? As far as Carnival should and could have known you were both the parents. The only problem then lies at home with the childs mother saying that you kidnapped the child. The solution to that problem may be resolved be sending the mother a certified letter(or 2,,maybe even 3 letters, no judge will agree that she didn't receive one of them) stating that you are taking the child on a vacation out of the country and if she objects please respond before(date of travel). If no response is received by that date I will assume that it is not a problem. We will be returning on (date). If she returns a letter saying the child can't go at least you'll know where she stands on the matter.
First of all you have to do it because the law says so.
Will you get caught? probably not. I can think of one other unknown.. the child. Will he/she agree to lie. Or if asked will he/she say no that is not my mom.