According to what I have heard from other people who have cruised (we have not) with 13 year olds...there is no official sign up for The Stack...correct me if I am wrong anyone... but the advice I have been given for my 13 year old is that she should just go to the Stack on the first day and plan to be in that group. In your case especially - since she has a sister!
The CMs in The Stack have a list of people who are in their age group. They can choose to card if they wish. You are much better off being straight with them--go to The Stack and explain the situation. They will assess your daughter's maturity and take into consideration the number of 14-17s on the cruise. Chances are that they will allow your daughter in if that is what you want. My point is that you should seriously consider whether this is best for both girls.
No one scans a card when you go in or out of The Stack. Yes, your card is coded with month/date/year info, but they're not looking at The Stack. yes, there are sometimes younger kids up there, particularly in family situations.
There are "rules," but the CMs have the authority to make exceptions.