I am from the US, I guess I just spell travelling weird.
First off, what is a notarized letter necessary for? If I am walking on the street here, no one will stop me and ask for a note. Is it a legal requirement to have one? Is someone likely to stop you on the street and ask for identification, or is it more customs and immigration?
I read other places that the problem with a hotel is the contract you sign, when you are under the age of majority contracts aren't binding. Do they really have a reason to care though as long as you have a card?