I'm sorry but this is NUTS. If she's stalking you, there is a problem. If I were you I'd quit the job.

I have a feeling if you indulge this woman, she might turn out to be really crazy and things will get much worse than you think. Every single person I've talked to who "caved in" to a person who stalked or pressured them had a relationship that ended badly. I was friends with one woman in particular who, now in her early 50's, has never recovered what she had after the relationship ended.