Hello and welcome. I am so sorry to hear of your mother's problems. It was in similar circumstances that we came to be Casper's guardians.
As I am in England I cannot help with the rehoming but I am sure someone more local to you will be along shortly with some useful advice. Veterinary Surgeries may be able to offer information on shelters for the birds if you are not successful in finding loving homes.
Oh, and if passing the birds to a stranger it is most important that you see the place they are going to live to make sure it is suitable.