Some people will immediately suspect a "weasel". I (living near Macon Ga.) have thankfully never encountered a weasel and I know very little about them. They are apparently bad news.
Snakes and hawks I know pretty well. They have been my main predators. Snakes are in some way connected to rodents but not just.... For rodents, I have a few cats and I also put out a bait station with some bait cakes in it and that will kill your rats/mice without subjecting them to the drowning pool. They generally eat some, go off and die, and that is that. Snakes will hide but will generally return so keep your eyes peeled. Your birds are evidently young... young birds are vulnerable to a lot more than older birds... hawks love youngsters. Snakes,,,, anything would eat a chicken, will doubly eat a young chicken. I find that it is helpful to train the birds to come when you call them. You do this by keeping them hungry and then, giving them a treat, usually in the same area, an area that is convenient for you. (I do mine in front of their coop) You put the treat in a can and shake it, then give it to them. They will get to where they will come when you shake the can. Can be handy. Picky eaters mean they are not that hungry. Which is ok. But for getting more control of them treats can be handy. Mine will come running when they see me, which is somewhat inconvenient, but if I need to put them in. (say a strange dog was in the front yard and I want them in.....) keeping them on the hungry side, I open the door, throw the scratch inside the coop and within two minutes, they are all inside.
Work on your rat issue if you have one.... but also keep an eye out for a chicken snake will be attracted to the eggs too. Work on sealing up your coop. Getting your birds a little more organized..... there are a lot of things you can do.