I mean, the idea of having to get rid of this chicken is actually pretty devastating to us. I'm glad you find this funny, but I'm asking for help here.
I get that she's part of the family. I get that she's a pet.
I get that it ticked you off. Been there, done that ... believe me.
I don't really find this funny at all and I suppose the point was lost on most...when the tables were turned there, it didn't seem quite such the thing to do did it?
Here's the reality...
Chasing her, pecking at her, poking her with a stick and withholding treats, what is that gaining? This behavior is going to frustrate not only you, but the pullet too - stress is not good for anyone. I doubt she even understands what or why you are doing all this. And the route you're taking - It's not something you want to teach your kids is it?
If you don't want to get rid of her, then don't. Keep kids out of the pullets faces, you may find that is the solution you are looking for.