From the sounds of it, the only way to stop them from breeding is to separate them into their own cages.
The hen doesn't sound like she is being a very attentive mother if she is throwing the chicks out after only two weeks. Who is looking after the chicks at this time? Are they being hand fed?
It's very bad for a budgie's health to breed over and over again. Laying eggs, incubating them and raising chicks is a LOT of hard work on both the male and females. Letting these two breed should be discouraged at all costs, or you will risk losing their health and risk losing the babies as well.