[....does Katsuki say "yes" to this and enable a small child to be violent? Or should he be a good older brother and try to steer her off this path?]

I say it depends on how bad they hurt 'em. And also it's usually a thing that only adults are s'posed to do to get revenge.

[He can hear Mike telling him off now--]

But sometimes kids are allowed to break legs too if they're up against someone who really deserves it.