It sounds like your daughter is taking her clues from your reaction.

When I was maybe 9 my grandmother took me for a haircut that I had been begging for. It turned out much shorter than I asked for and I was okay with it until my mother freaked out over how “horrible” it looked. I was mortified and will never forget how she made me feel about it.

This is obviously not the popular response but I think you are an asshole for making your daughter embarrassed of her hair and for making this something you would miss your mother’s wedding over. It’s just hair and your reaction is ridiculous. From your other comments it seems your daughter wanted a Billie Eilish blonde and it didn’t turn out right, but the blonde was something she wanted. So fix it instead of destroying your relationship with both your mother and your daughter over some childish power struggle.