cats and a bird ?

Ar

soo, I'm 15 and i have two cats that i adopted back in September, Sassy and Toby. they like to bring me dead animals such as birds and mice and lizards etc. , and my mom has decided to come home with a small conure, her name is Kiwi . and its been about 3 weeks I've taken every necessary precaution, like having a strong sturdy cage , in a corner so that it wont tip over. her wings are not clipped and i never leave my cats and the bird alone together. we had the cage completely set up a few days before the bird came so that my cats would be used to seeing it. and they've been fine around the bird but she's so social and never wants to be in her cage she always wants to be with the kids so it worries me with my cats I'm afraid that they will kill her and bring her to me . My dad has already told me that if i cant get my cats under control then hes going to shoot them. Now , I've trained with my service cat who recently passed , she was okay to be around mice and birds and rabbits and everything but i did have her since birth.

if anyone has any helpfull tips on how to solve my issue here , please let me know i really cant go without my cats they keep me grounded .