You wrote:"The basic (rabbinic) rule is that one person may not carry into the property of another person unless there is an Eruv Chatzeirot. " Based on this I am unclear as to how you may carry in a hotel. Is it because the hotel belongs to another person, but you are not leaving that domain?
Thank you for the clarification. The entirety of the hotel belongs to the owner of the hotel, including the rooms that we, the guests are renting from the owner, so when I carry around the hotel I am carryiong within the property of that owner. The room I rent in the hotel is not my property unless it is a long term rental and all the movable object belong to me, otherwise I am simply a guest in his home.