I am a twin with a brother and we were in the same class for just about EVERYTHING until the end of our high school (in the US). The high school we attended had a general policy of separating twins but we were both in an "honors" track, of which there was only one group per year, and our academic advancement took priority (quite rightly) over our being separated.
Nevertheless, I felt every moment that my twin bitterly resented having to be in the same class with me for everything (though we did use it to our advantage sometimes to divide up the homework - "you do the Spanish, I'll do the math" etc). He was a teenage boy who HATED the fact that everyone thought the whole "twin-thing" was SO CUTE, and it called attention to him at an awkward time when he preferred to just blend in and conform. At the same time, most of the time I did better than he did academically. He knew it wasn't my fault but he sometimes couldn't help taking his resentment out on me, or freezing me out with complete indifference. And it hurt. We went to different universities and have lived completely separate lives ever since - I now live an ocean away from him. We get on fine with each other now (we are in our late 40s) but I wouldn't say we have a special "twin bond" and I don't think he would either. We're no closer than any brother or sister.
If you have a chance for your twins to be separated and you don't take it, one or both of them will come to resent it, as well as possibly you and each other. That is pretty much guaranteed to ruin whatever twin bond they have now.
If one twin is struggling with the separation while the other isn't, you just have to give as much support as you can to the "abandoned" one until the other twin comes round, which if she is given her chance to get out on her own and do her own thing, will happen.