OH!, you poor thing, I feel for you and your birds. I've had those little buggers, and they are nasty, and persistent. You don't mention what kind, so I'm assuming they are red mites??
If your babies have mites, then it's more than likely the other birds too

I've had red mites and feather mites, and both are difficult to get rid of.
I've used A.I.L.(Avian Insect Liquid) with EXCELLENT results, killed those little buggers! thank goodness.
I've purchased it from ladygouldian.com,located in California, you can try SCATT or S76,as well, but personally I think A.I.L. is more effective.
with the holidays around the corner, you may be stuck trying to find some... unfortunately I don't have any home made remedies.
could you contact any local breeders and see if they have some?
the sooner you treat them the better, they multiply 10 fold, and will make your babies miserable.
here are some things you could do to combat them until you get treatment
thoroughly clean and change cages daily, remember to check under the tray
boil toys and perches for 5 minutes, then put in the dryer on high for 20 minutes daily.
remove any toys for now, and only put in perches, and seed cups.
make sure you wash your hands before and after you handle your babies.
purchase iron drops, and add 1 drop into their water daily...they become anemic, then paralysis sets in. I had 3 birds go that way, then I thought of the iron drops, they were all back to normal within 10 days!!...it was amazing to watch
I sure wish you the best of luck.