I have had one hen that would open an egg and eat it, only one hen out of all the ones I’ve had. It is pretty rare but it can happen. When you are dealing with living animals practically anything can happen.
How thick are the egg shells of the ones that are eaten? As HE mentioned it is perfectly normal for a chicken to eat an egg that is already opened. That’s not an egg eater. The egg eaters are the ones that purposely open an egg to eat it. Not all chickens will eat an opened egg but most will if they are really opened.
If the egg shells are really thin, it is not that hard for them to get opened. They may crack when laid, a claw may poke a hole in them with a hen walking on them in the nest, or they may be so flimsy they get crushed by her weight. So check your egg shells. If they are really thin, that is probably at least part of your problem.
It does sound strange that something like that would happen in two different nests in the same day. That means two different hens are laying extremely thin shelled eggs. That’s not likely. It really doesn’t sound right.
It could be a hen opening the eggs. I don’t know how well that coop is protected, but it is possible a rat or something else is getting in and eating eggs. It’s really hard to keep some critters out of a coop. They really don’t need much of an opening to get in. Even if you leave an egg in there, if the same thing happens then you will still not be sure that it is a chicken or something else. Instead of just leaving an egg in there, you might try putting an egg where the hens can see it and see if one opens it. Be patient with this. I’ve put eggs in front of hens before and they go over and inspect it, even peck it some, but they didn’t open it. They were not egg eaters, just curious. This stuff can be hard.
If you do have an egg eater, a hen that purposely opens a good egg to eat it, you will get all kinds of recommendations on how to fix the problem. I personally have confidence in only two methods. Either permanently remove that hen from the flock or build roll-out nest boxes so the eggs roll to a place the hen cannot get to them.