That twiddling and touching drives me crazy too! I think it is common. There are a few threads about it, if you want to search.
I take her hand, and hope she holds that instead, and sometimes it works and sometimes it doesn't. If she gets too insistent on twiddling where it is uncomfortable or starts pinching, then nursing is done for us too. I explain it to her. It is ok to set boundaries, and teach respectful ways to nurse, especially as they are not tiny babies anymore.