Hi Julia,
You may be confusing the by letting them out. When birds are breeding, they need quiet and privacy and no distractions. By letting them out of the cage, they are leaving their nesting area, and the female may be viewing the male as an intruder when he leaves and returns. A breeding pair of any species can be very sensitive to changes. It’s best to have them in a low traffic area and avoid going near the cage other than to feed them. And definitely stop letting them out as long as they have a nest and eggs. Try giving them privacy, don’t let them out and see if the female settles down. Otherwise they may end up killing the chicks if any hatch. Some pairs do not make good breeders or parents. So see how they do, but if the fighting continues, it is possible this pair isn’t very compatible. If the eggs do not hatch, remove the nest and do not give it back to them for a few months. In the wild, they only use a nest during breeding season. In captivity, the same goes, but the problem is it is ideal for breeding year round indoors. So you have to take the nest away to make a pair rest, and you should limit them to 2 clutches per year. If they fight even without the nest, then I would split the pair up.
Thank you for asking Lafeber,
Brenda