Lol your sister is so amusing.
All she had to do was say no. It’s not that hard.
Honestly if it wasn’t for the fact she drives I’d have guessed you at about 18-19 years old, and her at about 13-15. So it’s super funny when she accuses you of being immature. And literally using your age as if it’s an insult - wtf is that?
Also she accuses you of making it all about you, when it was planned by your dad, it was known about ahead of the trip, all you’ve done is ask for a lift, and she’s the one that says “I might I wanna”, instead of just a polite no.
But you did get into an unnecessary argument, and it took both of you to do that even if she was the most immature about it.
If I were you, I’d just be more matter of fact in future. To her first message back, just say “Okay I’ll take that as a no; Thanks anyway, see you later”. Then make other arrangements to get yourself there.