Hello, StrayJoe, and welcome to the Parrot Forums family. I wish it could have been under better circumstances.
That looks like a terrible injury and will quite possibly be fatal if not treated by a vet. I can't stress enough that if your parents can, those injured birds should be taken to a vet. Or, failing that, they should perhaps be surrendered to a local avian sanctuary or some such who might be willing to care for them. Keep in mind, also, that some vets might be willing to work with you and your parents on a payment plan.
In the meantime, first thing you need to do is separate the mother from the babies. And then work to stop the bleeding. Corn starch can help with this, or flour if you don't have CS, though you'll have to be VERY careful since the wound is in such close proximity to the budgie's nares. You don't want any inhalation of that stuff, as birds' respiratory systems tend to be very delicate.
Again, this really is a job for a vet.
How old are these babies? Are they eating independently of their mother just yet? Are they on solid foods? If not, you will also need to take over feeding using bird formula. Respond as quickly as you can, and hopefully one of our site's breeding experts will be able to help you out as well. The temps for the formula are very important as well. Too hot will burn their crops. Too cold will risk the formula hardening in their crops.
I'm hoping the best for those babies.