It certainly would not hurt to bring along a copy of the official record of whatever event caused the surnames to differ. This might be, for example, your marriage certificate if the difference arose because you remarried after their birth or their birth certificates (showing that you are the mother) if their names have differed from yours from their birth. If any questions arise, such a record will provide clear proof of the relationship.
If your husband isn't their father you are going to need a letter of permission from their father to take the children from the country unless you have prof that you and your husband have their sole guardianship. You will need to take proof of that. Most of the tie the cruiselines don't even bother looking at anything other than citizenship, but you njever know. Better safe than sorry.
If you are divorced Princess requires that you bring a copy of divorce papers. This is the first time that I've sailed with them and my TA srongly advised that I have a copy with me when boarding.The child in question will be 18 in Dec. and we sail in Nov.
I went to mexico a few months ago and had to have a notarized letter from my child's father giving permission for them to leave the country. They informed me that had i not had it my children would not have been allowed to go. I was lucky as my travel agent informed me ahead of time and I had my letter.