I don’t see how her story is inconsistent, but that’s just me. So what if you saw her car?
I also don’t quite get what’s so damning about her car being at her favorite hangout (wouldn’t that be, by definition, where she most likes to hang out?) but whatever. About revenge, phrase it this way:
1: This person has acted in ways that caused you suffering.
2: Therefore, you would like to cause her to suffer.
3: In other words, you would like to be the kind of person she is.
If the idea is still appealing after phrasing it that starkly, if you’d like to be the kind of person who enjoys making another suffer, who enjoys seeing another’s suffering–then by all means, go ahead.
I think the kind of person who enjoys that is somewhat horrible, but variety makes the world go round.