Does she give you nay trouble when you take her away?
If she does, prancing, constant whinning make her work serpentines, circles giving to the bit, after about 5-10 minutes try and do what you were doing and if you get road blocks again go back to making her work. She will soon learn its easier to move away then it is to be focused on her buddy.
As far as isolating her I dunno, I wouldn't like it and she might get herself all nerved up, like it has been said above its natural to want to be with ur buddy the one that makes you feel secure, feed off that. Show her you can do that also work with it don't punish her for it.
I am training a buddy sour Standardbreed, with the same issues like were talking FREAK OUT, rearing all that. Its been 2 months and the owner came out the other day to go for a walk with us and she could not believe it was the same horse. It takes time and patients and some days are better then the others.
Live to ride and ride to live!