If she is copying your boss on emails she sends you, your boss may see her passive aggressiveness as unprofessional and immature.

Why does your boss want the 2 of you to go to dinner?

Let her spread rumors. Do your job and prove her and everyone wrong. It appears you're in the middle of office drama. How do you know she is spreading rumors? If someone is reporting back to you about her, how healthy is that for you?

Consider finding ways to feel better about yourself. you seem very caught up in what this woman and others think. And I get that. I'm like that too. But when we are secure, that stuff falls to the wayside.

Does your boss know what's going on?