I don't have twins, but there were identical twins in a class above mine from 5th-12th grade. I don't know if they were gifted, but they were always very good students. They were always in the same classroom (and fwiw, dressed in the same way), and I remember some issues along the lines of "my sister had an A-, I have an A, we need to have the same grade" etc. (this in a school abroad where failing was very common, and grade grubbing was unheard of, except in cases where an F meant repeating a class). Several years after graduation, I heard that they dropped out of medical school because they couldn't get a residency in the same hospital. And they started law school, to then have a similar issue with internship location (med and law school start right after highschool). I don't know if they ever finished anything. I also don't know if these girls had been better off in separate classrooms earlier in their lives - but I suspect so. Just a sample size of one to keep in mind that separating identical twins at any stage can lead to issues. Perhaps there are studies that follow identical twins beyond college?
All that said, clearly here fit with a teacher is a major problem, not necessarily the twin question - and as has been said above, they might threaten to put both in with the worse teacher if you focus too much on the "twins together" aspect.
