You've never met my 7 year old. Girl holds a grudge against me for trivial things I did or said over two years ago. I'll be hearing about how I got rid of her favorite chicken for the next 25 years.
Yikes. I know you know this, but that's gotta be nipped in the bud before the teen years or you're going to be dealing with a very unpleasant and controlling person.
In my family, I'd explain why he has to go then tell her that any whining means all the chickens go and we will not be getting more. Your kids shouldn't be afraid to express their opinions around you but they should think twice about disrespecting your authority. Especially with stuff that is past. Just two cents of my opinion, I don't intend to tell you how to raise your children.
Or maybe you could stage an animal attack, like go out for a day/night and have a friend take him and say he was taken by a hawk or something while defending his hens like a good rooster so they remember him as a hero.
Just a thought.
Chickens are hard pets for kids since they are:
Bottom of the food chain, everything wants to eat them.
Jerks, chickens will pull other Chickens feathers and bully them. Flock politics can get deadly.
Males can be loud or aggressive, even hormonal hens will bite.
Just one more thing, if you have the prefab coop with the nest boxes that you get into from the outside, reinforce the bottom (floor) panel of the boxes, my friend lost her chickens to coons that popped that up and got in the coop that way.
Good luck finding a home for the feller.