She sounds like a very smart nine year old who has figured out how to run the show, make you dance on a string, and get under her Dad's wife's skin. She is very successful, isn't she?
Normally, smart nine year olds will try to get their way, and good parents know that they are not ready to rule the world. I would absolutely disagree with you that the whole vacation revolved around her, it revolved around two adults who gave into a nine year old and who are looking for reasons to blame her for this situation. It would be much easier for you, if we would all say that this child has a developmental issue that exhonorates your husband from being able to take control. I don't see anything like that in your post. Quit blaming this little girl for the mess her parents have made.
I don't know what your diciplinary situation is as the step parent, but the person you need to be talking to is her father, and he needs to set some limits and be willing to let this child be unhappy once in a while. THAT is normal. Nine year olds are unhappy A LOT because they can't have everything they want, and THAT is just fine. Let her sulk. Let her have a bad time. Leave if she can't behave herself! Parents reap what they sow, and if you stayed so that YOU could have some fun and tolerated this behavior, you put a big rubber stamp on the continuation of the behavior even worse for next time. You will only have to leave one water park and she will catch a clue. She caught a BUNCH of clues, all of them are really bad for her, and the biggest one is that you are a helpless victim who can't do anything about this but vent about how bad she is. Parents have to make sacrifices, no it is not fair, but that is part of being a parent, and when you are alone with her and Dad, that is what you are, so start making sacrifices for the sake of her character development or quit griping about the result. Parenting is hard, and it is not about YOU having a good time. If you had an ablsolutly horrible trip to the water park that ended far too soon and taught her a long overdue lesson, it would have been the best vacation ever.
Have a talk with your husband and her mother. This cannot contine and you all need to be on the same page and help this poor girl learn to be a young lady. If someone actually applies good diciplinary techniques for this child all the time, and she cannot manange to change the behavoir, then you can start to question if she is typical or not. You all are not there by a long shot.