How DARE your MIL do this. I'd be FUMING were this me.
Nah...just kidding. I sincerely feel you at totally overreacting. Your daughter is 15 years, not 15 months and it's her body (well, mullet) and, thus, her boundaries.
A "severe" haircut? Really?!
Bloody hell, if your MIL had taken your daughter to a crack den, I'd understand your anger, but come the fuck on...a 15 year old getting her hair styled to her liking? Check your conservative, internal prejudice, as you think she might be bullied for a pretty commonplace - if very 2020 - hairstyle?!
If her school classifies an haircut that a male student wouldn't be pulled up on as 'extreme' and places her in isolation, I hope she has the confidence to challenge this, as Mummy clearly isn't in her corner.
I'd drop all pugilistic fantasies agin MIL, try to haircut shame your teenage daughter and maybe consider some restorative meditation.