Earlier quoted context omitted.
If she really wanted to see the movie with you, but she actually had to take her dog to the dentist, she would have counter-offered a time and date. She was trying to brush you off, hoping you'd take the hint, without appearing confrontational. It obviously didn't work. You continued with the unwanted advances, and it made her uncomfortable.
I actually ended up asking her what was going on, specifically, "Am I bad at taking hints?" At that point, I should think a simple yes would have done fine. Making someone feel like a rapist for believing what is said or failing to correctly second guess is just weird and oppressive in itself.
It is unfortunate and I sympathise with your hurt feelings, but I think this is just something you should take on the chin.