It's not fair that you're being treated poorly, but it's also on you to make sure people treat you with basic civility. Having a speech impediment can make you feel like you're less than others, but I guarantee you, if you allow it to go on, you will feel far worse than if you'd done the uncomfortable thing of confronting her. My advice would be to go to a higher up and request a sit down, if they refuse or she doesn't listen, confront her directly and ask her what her problem is. If you're a man, handle it a bit more carefully, as she could easily play the "I felt threatened card." Sadly in this world if you don't stand up for yourself the arseholes will pick at you to uplift their own miserable existence. Best of luck to you.