I had the exact same thing. I have not read all the replies yet, so if covered already sorry.
I had my chickens in a pen area that was made with 8' tall chain link sections.....off the top of my head about 12 of them. This had a big plus of being "sort of" moveable....more on that later. On top of it I had a nylon net to keep hawks and owl out, learned that the hard way. Around the outside I had the fence setting on concrete pave stones so the furry four legged critters could not dine at the all you can eat chicken buffet. It is a never ending battle, I have seen them scale the fence chew through the net, and go down the inside like a little commando....you are always upgrading. Suggestion a rooster will die trying to defend his girls, but he will bring other things that could be good or bad, a fresh supply of new chickens, his attitude to you or your wife and kid is also likely to get him killed.
On to the gun, this is why I bought a 38-357 lever gun, this is enough for the largest mammal (Coyote) that I had issues with, is not so over powered as to be an issue no matter what direction I shot like a center fire rifle would be. I am shy on 22mag on a coyote, I want a sure fire ethical kill, and the angles and stuff in the way I just wanted more error on my side.
I said I would cover the moving the chicken area, all I had to do was hook the tractor to the fence and drag it, I used a couple long tow ropes on edges, after you remove the concrete pavers it will slide pretty easy, my chicken house was on wheels so you could roll it to the new spot to let the grass recover. I really could not let the chickens, and really chicks free roam because all the birds of pray I have around my house....and you can't kill those.