Need help by tomorrow morning?

About 6 weeks ago, a coworker and I were up for a promotion. I ended up getting it, though she had been with the company longer. What has resulted has been 6 weeks of talking behind my back, rude comments, sarcastic conversation, lack of respect, and undermining my authority. I am her immediate supervisor now and she can't seem to respect that. I can understand her view: 6 weeks ago we were merely peers and she had seniority. But I need to take charge now, upper management is starting to notice and it's making ME look bad that I can't stand up to or keep my employees in line. I went to my supervisor today with all of this and she is going to get written up first thing in the morning. We work in very tight quarters and I'm unsure of how to handle this. How do I let her know that I mean business from now on and that I won't take her blatent disrespect? How do I handle her after her write up when she comes back and we have to continue the rest of the day together? Thank you in advance!