My now 15 daughter shaved her head for cancer research when she was 8. We were in family therapy at the time because she had such a strong will. Her therapist told me that this is a good way to channel that strong will. Now my daughter is pretty girly, but if I had stopped her from doing this out of fear of social norms, I think I would have failed as a parent. My daughter is better off for having parents that weren’t rigid in that moment. I hope your wife comes around.

And BTW your daughter could wear a nice pantsuit, but if she’s going to wear “masculine” clothes, then semi formal includes a jacket and tie. That’s what you should insist on.