Remember it is easier to ask for more and get less then to have not gotten what you truely needed to cover your loss. You have a coop to repair as well as birds you are out. Then consider that you are out eggs, chicks, and probably more. This is what will help you make the point that this WILL NOT happen again. If they balk at it remember that small claims courts do exist. You are not asking to much of your neighbor just that they mind their business like you mind yours. i have been on both sides (sort of) for this story. I had a neighbor's cows that got out and destroyed my garden as well as some property. They did offer to pay (later), but to this day (2 years) don't speak to me more than anything because I got mad and stood my ground do to their neglagence.
Now for the other side. As well as chickens I am a dog breeder (American Bulldogs) 120 lbs of spoiled puppies. One is snoring at my feet as I type. They would harm much of anything but are a typical animal and if they can get out they will. hey have "gone to visit" but never ever damaged anything or anyone, but I always imediately offer to repair or replace anything that they might have damaged just like I do when my kids get out, haha. Your property ois your responsibility and you should own up to it just like they should.
Look for pay back for their actions but also look for long term effects. You may get what you ask for in payment but you may also get what you didn't by being isolated by you neighbor. This is a choice that you need to decide. Maybe you can look into have them help you repair you coop as then offer to help them "confine" their animals.
Good luck, you are in a rough spot!
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