Thank you all so much for your replies! I am going to to sift through them and try them out.
I've only had her a week, so it's still all very new. I can't separate her completely, but I do put in her a paddock that's attached to her main pasture during the day. It's a large-ish pasture and her pasture mates will often move to the opposite side, so she's not right next to them, at least. At night, her pasture mates go in the paddock and she goes in the pasture.
Yesterday I worked with her in the paddock. We practiced walking without getting in my space, and stopping when I stop. We worked on backing and yielding her shoulders and quarters on the ground (quarters great, shoulders we need to work on). She was doing wonderfully by the end of our session. I'm hoping that if I take baby steps and slowly start moving farther from her herd, it will work. If not, though, the tying out may be something I need to do.
I do have someone that specializes in groundwork training coming in a couple weeks to help. I have a hard time knowing how to correct her and doing so quickly enough!