Relationships with step-siblings can be difficult, especially in your teens, you generally old enough that experiencing a true sibling upbringing is out of the question. It doesn’t mean that the two of you can’t grow close but that whole sibling ingrained love/hate thing is sort of out of the question. Which also means that instead of begrudgingly accepting the presence of your younger siblings—even when they annoy you—you’re more likely to just get fed up with a stepsibling and want to have nothing to do with them altogether.
Of course, though, it depends on the people and the circumstances involved, and you may come to understand each other as siblings no matter what age you first meet, but as with anything you can’t force these things and it has to naturally develop on its own with time. Simply because «step-sibling» has the word «sibling» in it doesn’t mean it’s automatically true. The fact that the teen refers to her stepmother as her «dad’s wife» tells you everything you need to know about her feelings on the situation.
Adding to this, it’s not really your place to invite people to places that you have no involvement in as this dad and stepmother have done here. In any social setting if you’re not hosting, it’s always essential to ask the people who are hosting or planning the event for permission before bringing or inviting a plus one or 3rd party. It’s pretty crazy that these parents just told her stepsister that she could go with the woman and her friends when they had nothing to do with the trip or its planning in the first place.