Hi! Exciting birthday for your twins!! I've been to Cozumel twice now and I wouldn't worry about the other country thing. The ship ports in a fairly touristy location. Its very easy to get around. I would honestly say its the same as bringing another child to any US city and in all my reading the crime rates are likely less than any US city. We have a family of 5 and had no problem finding a taxi that fit 5.
However, if you simply don't want to bring another child on your vacation day or if it makes you uncomfortable then don't feel bad saying no.
I am very familiar w/ Disney's policies on bringing kids on and off the boat because we always book two connecting rooms for our family of 5. Without that paperwork I can't even bring my own child off the ship if they aren't in my room, even if they are in my husbands connecting room. To me the policy is crazy as the reservations should be connected and I am their parent, but we won't go there. Anyway I have had an issue once in which the paperwork I turned it wasn't showing up when we went to leave the boat so now I ask them to make a copy for me when I turn it in at guest services and bring it with me in case there are any issues.
