OMG - she'd hate that. She is the leader and when she can't see or be by the other two she squaks really loud. But it may come to that to get to the bottom of this mystery.
How about crating the other hens instead? Or sectioning them off, so they can still see each other, just can't access the same nest boxes? See what happens then.
I have heard of people saying one of their birds laid two in a day but never three. The most I ever got was double yokers. Tis a mystery.
Maybe some kind of a camera. I bought a camera system with a DVR. I can put a camera out in the coop and watch on my computer or TV. My 19 birds are banded. They each have a different colored band on one of their legs as they are all one breed. My first system was a single camera. My newer one has four cameras. All record at once. you can watch all cameras on one screen or you can view each cameras video and capture any part to a picture (jpeg/jpg/png).