It's usually possible to style short hair so that, from the front at least, it has the look of an updo. Unless the sister really wants long tendrils on her bridesmaids, it should be possible to mimic the overall look and feel of the hair style the sister really wants.
So that's a compromise the OP can offer her sister. Get the haircut, wait on the highlights, and agree to style her hair to look as much like the other BMs as possible.
In general, I come down firmly in the camp of bridesmaids don't have to have the same hairstyle. But in this case, there's a delicate balance between what the two sisters each want, and overall family harmony. While I don't think the OP needs to give in to every last demand made by her sister, yielding a few points here and there where she can may go a long way to keeping the peace.
And I think Toots made a very good point. If the sister really doesn't want purple hair in her wedding party, having pictures with that purple hair in her wedding album may only serve to remind her, over and over, of what the sister might see as a deliberate slight.