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I will be going on a cruise with my boyfriends family in January. I will be 18 at that time, I know that you can drink at 18 with parent/guardians permission. Will I be able to drink on the ship?
Take a look at Norwegian's Guest Conduct Policy. As you said, it states that a parent or legal guardian must sign, but it also says that said parent or legal guardian "must be onboard" to sign this consent. "Parent or legal guardian must be on board to sign consent for beer and wine." Since "your" parents are not on board, they cannot sign consent for you, nor can your boyfriend's parents.
Which bring up the question, what about your "consent" to be on the ship at all, since you are 18 and your parents are not on board? Maybe you already have this covered. If not, I would check it out as you might be left waiving goodbye from the pier otherwise.
Back to the beer/wine consent question, the policy further states that even should your parents give temporary guardianship to the BF's parents, or you bring a notarized consent signed by your parents, it is not accepted to allow the beer and wine consumption: "A notarized Parental Consent Form or any other document allowing for Temporary Guardianship for the purposes of the sailing will not be accepted.
So it sounds like you cannot get permission to drink.