From an anatomical stand point a slight correction.
The things you described as 2 eggs are not eggs at all. They are male coturnix sex organs. They look a lot like eggs but they are really male sex organs.
Coturnix hens, like most Galliformes only use the left ovary to produce eggs unless it shuts down for some reason. If that happens then the right can kick in and a strange hormonal shift can happen and the hens will start acting, sounding, and even looking like roos, but that is rare.
I can get confused with the vent sexing thing, but if you split a coturnix down the back its pretty easy to sex.