I wouldn’t bother. It’s rose tinted specs at work. Girls on the horse yard bully each other just like they do in every other arena. Source: I had a horse when I was a teenager.

The OP was painting an incomplete picture, the complete horse based solution to bullying involves plate mail and polearms.

I’m afraid this is also a case of ochre-tinted helm — girls will bully each other even if their liege lord fully equips them.

So they can push the kid over and it ends up stuck lying on its back like a turtle?

Really? It seems obviously complete nonsense to me.