This has nothing to do with your problem and is just my personal preference, but it's a reason I like my walk-in coop where I walk in every day to gather the eggs. I see things I otherwise would not see. I know others really love their nests where you collect the eggs from outside. With many coops you don't have a choice. As I said, a personal preference and nothing really to do with your problem.
It's not unusual when a pullet first starts to lay for her to lay weird eggs. Putting an egg together in her internal egg-making factory is pretty complicated, some pullets take a few days to get all the kinks worked out of that system. No shell, thin shell, really thick shell, no yolk, no white, double yolked, or a perfect egg but tiny are just a few of the things you might see. I don't worry about a few weird eggs when they first start to lay and would not in your case. Since there were two good eggs she may have already got the bugs worked out. Or it could be a different layer.
I'm not sure why those eggs were on the coop floor, could be different reasons. It sounds like they were all in one place. That means she sees that area as a nest. Sometimes when they first start laying they accidentally drop them wherever they happen to be, from the roosts or just walking around. For these, this is another kink in that egg laying process they need to straighten out.
They often like to lay where another hen or pullet is laying. Putting a fake egg in the nest you want her to use can sometimes help. I'm using words like "often" and "sometimes" because some do like to to follow the crowd but some like to do their own thing. I use golf balls but you can get ceramic or wooden eggs from a craft shop that look really real.
The way I'd approach this would be to make sure there is a fake egg in each nest you want them to use. I'd make sure eggs did not lay on the coop floor any longer than they have too, I've had a second hen start laying there too when an egg was scratched out of a nest onto the coop floor. I've never had any success blocking where they are laying with a box or something, they just move the nest to next to that box, but making it not look like a nest is a good thing. Then I'd give it some time. Photos of your nests and the coop might help give us some other ideas if she doesn't move on her own. It's hard for me to give too specific suggestions when I'm not sure what you are working with.
