Picture this example:
You are having fun!!
And then splat!!!
You just walk over doggie poo.
I have two dogs I love them as my sons but I don't think the will have fun on ports
What are you going to do?
Leave them on your cabin?
What happen if they bite someone like the ones that work on your room service?
What happen with the cabin next to you, your neighbors which ones had pay good money for their vacation too, if they start barking during the day or during night?
I will tell you my point of view:
You can have a lot of trouble just for getting the dog inside the ship, but you can have more trouble when you are at sea and people start complaining about your dog, sadly Dogs are nice but not everyone is a Dogs person so you know you will have troubles anyway.
IF I were you I will just leave them with someone that can take good care of them like I do during my cruises…