Hi Nass,
When you are breeding birds, you can only have one pair of birds per cage. Once a pair has a nest box, they will become territorial and will attack any extra birds in the cage. Even if they seem to be getting along, this can change in an instant. When a budgie attacks another, it can come without warning and a budgie can kill another budgie in a matter of minutes. In your case, you should not take any chances and you need to go ahead and remove the third bird. Even if you do not plan to breed your birds, it is never a good idea to have an odd number of birds in the same cage. Birds will tend to pair off, and the odd bird out gets ignored and bullied. It is very stressful for the odd bird that doesn’t have a companion.
As for your white budgies, just because one bird has laid an egg, doesn’t mean that the other bird is a male. In captivity, two males or two females will often bond and even try to mate with each other, and behave the same as a bonded male & female. With the white budgies, most are female, although it is possible to have a white male. You mentioned the birds are young, so they may not be old enough to be laying eggs and have a nest box. Birds will become physically mature at too young of an age in captivity, but they are not really ready to settle down and handle the rigors of hatching eggs and raising chicks. Your birds need to be at least a year and a half old before you give them a nest box. Otherwise the female is at a higher risk of becoming egg bound and dying, and both birds are more likely to develop bad breeding habits which will prevent them from being good breeders in the future. If your birds are not at least a year and a half, then you should take the nest box away until they are old enough. It sounds like they really are not ready to breed since the one bird is laying eggs from the perch and showing no interest in the eggs. Since the Vet felt like they are both female, it is very likely they are, and in that case, you should never give them a nest box and instead make some changes to discourage egg laying. You can limit their light to 8-10 hours per day by covering the cage early each evening. Rearrange the toys and perches in the cage and move the cage to a busy place in the room. Birds need a good diet, long days, warmer temperatures and a safe, private place to nest in order to breed successfully. So to prevent egg laying, you reverse these conditions.
As to determining their gender, it is often not possible to tell the sex of the solid and pale color mutations just by looking at them. They do not exhibit the cere color changes that the other parakeet mutations have. The only way to know for sure is a blood test or if a bird lays an egg, you know that bird is female. So again, you only know for sure that one of your white birds is a female. If you really want to breed them when they are old enough, I would recommend asking the Vet about sending off their blood samples for DNA testing. You do not want to end up giving a nest box to two females or they will keep laying infertile eggs, and that is very hard on their systems.
Thank you for asking Lafeber,
Brenda