Magnificent BirdMan
Regarding your Cat Mama and kittens:
There are different treatments for Notedric Mange (otherwise known as Feline Scabies ) which is highly contagious, so if your Mama cat has it, the kittens have it as well. It is a severe skin infection, which will cause inflammation, severe itching, discomfort, and hair loss.
Descussing it with your Vet, would be your best option.
However.... if this is not an option.......
If you can get your hands on a product called EcoSpot, it might be helpful. It is made for dogs, but apparently is safe to use on cats as well.
It is sprayed on twice daily, then allowed to dry. Treatment I believe , needs to continue for a month, to make sure that you get rid of all the eggs, etc.
Good luck
Regarding the birds, I would treat their health issues, before worrying about a new cage. What good is a new cage, if you lose your birds to some illness? Right?