Are the eggs always laid in the same spot on the coop floor? Sometimes when a pullet first starts to lay she does not have good control over that process and will drop an egg wherever she happens to be. A lot have control from the start but several don’t. So it the eggs are scattered I’d say be patient. Or if she is laying from the roosts, she doesn’t have control so again be patient.
If the eggs are always in the same spot she has decided that is her nest. That’s a challenge. I made some of my nests so I could lock a chicken in there if I wanted to. That’s come in handy for a few different reasons. When I have a hen laying where I don’t want her to I catch her when she is on that nest and lock her in a nest until she lays the egg. Usually that takes about a half hour but I have had one take as long as three hours. Most of the time I only have to do this once but I have had some take twice before they get the message. It helps that I am retired and can go down there a lot to try to catch her laying. Not everybody has that luxury.
Something I have not tried but others have said it worked is to put a nest where she is laying, maybe a cardboard box or cat litter pan with bedding. Let her get used to laying in it. Then gradually move that nest to where you want her to lay, just a short distance every few days. When you get it to where your nests are remove it and see if she moves to your nest. At least you don’t have to be there when she is laying to try this.
Another option is to build a nest where she is laying and call that good.
One thing that has not worked for me is to block the nest where she is laying and hope she moves to the nests. When I’ve tried that she just lays next to whatever I use to block the old nest.
I’m not sure why those eggs are being broken. If she is laying from the roosts they can be hitting something hard. Sometimes a pullet lays soft shelled or even no shelled eggs when she just starts, it sometimes takes them a while to get all the kinks out of their internal egg making factory. Those eggs are really easy to break. It’s possible you have a chicken that has learned to open an egg to eat it. That’s bad. Most chickens will eat an egg that is already broken, that’s natural and not a problem. But occasionally one will learn to open an egg to eat it. That is a hard habit to break.
