Related atiels Breeding?

I have four atiels and a Princess Parrot in an aviary. The atiels are all related (mum and three kids) and the kids are two years old in February next year. I'm not sure whether the kids are male or female but one of them is laying eggs and my dad said that they have been mating. As they are related I can't let them hatch, but I am really worried as she keeps laying eggs. I think it is the same bird laying them. She lays them in one of the seed dishes (a coop cup that is on the wire) and every couple of days there will be a new egg. I have only seen her trying to sit on the eggs twice but she has laid heaps of eggs. I get rid of them as soon as I find them but I really need help. Seperating them would have to be a last resort as they have born in the aviary and are a really tight flock, getting really distressed if one of them is missing. We don't really have a suitiable second aviary anyway and they freak out if they are in a normal sized cage.