Not sure what happend to the OP but if they are still around.......a question. Is the momma coon tree apart from the run area? Can they get to it without dropping to the ground? As in go overhead from tree to tree to drop down where they like?
If so and if they have to come down that one tree to get to the ground and your birds, no trapping or shooting is needed. Put up an electric fence between the tree and your coop. I'd use poultry netting for this. It will keep this mess of coons.........and the future coons that will replace them safely at arm's length and away from your birds. Half the cost of hiring your trapper and it lasts for years.
If so and if they have to come down that one tree to get to the ground and your birds, no trapping or shooting is needed. Put up an electric fence between the tree and your coop. I'd use poultry netting for this. It will keep this mess of coons.........and the future coons that will replace them safely at arm's length and away from your birds. Half the cost of hiring your trapper and it lasts for years.