Take another look at the sentence:
Closing the hotel room door and pulling the heavy suitcase to the elevator,
the relaxing beach vacation came to an end.
Closing the hotel room door and pulling the heavy suitcase to the elevator, a participle phrase, has no target in the sentence. When a modifier has no word to describe, it is dangling.
To fix the problem, you should revise the sentence like this: Closing the hotel room door and pulling the heavy suitcase to the elevator, Monica realized that the relaxing beach vacation had come to an end. Adding Monica to the sentence lets the reader know whose happiness has ended.