First, I am a breeder but not of caiques, so you will have to take my advice with a. Grain of salt, but I am experienced with co parenting babies.
How old is the baby? You say he is eating on his own and screaming for mom and dad, are you sure he is fully weaned? Often times parent raised babies don't wean as fast as hand raised ones, and as you know, there are serval weeks when the baby is eating solid food but is not yet weaned. It could be that your baby is so terrified, angry, and hungry, and confused that there is no way he can pause to even think about being your friend.
Is he around other birds? If he is fully weaned, consider moving him to where he can interact with other same species tame birds, and follow their lead on how to interact with humans.
How often did you handle him, and what kind of interaction did you have? At what point did he start trying to bite you?
Look at his posture; is it fear biting or actual aggression? Is he being territorial? Is it just you or all people? Does he stay angry even when he is in a different room?
What are you doing to tame him? Is this your first parent raised baby? If he doesn't think he is tame, then he isn't, and you will need to start from step one as if he is a wild caught bird. Caiques are a unique species that is known for being a very bold and demanding species, it could be that co parenting this species is just not a good formula for a good pet (even though I am very pro-co parenting in general). We already know that there are pretty major differences psychologically between hand raised and parent raised birds on a sliding scale depending on raising fledging and weaning techniques, but I am not aware how they play out with caiques. One example is that a co parented IRN almost never bluffs.
In the end, if all else fails, you can ask yourself if the physical health and personality of his parents is something that you would like to pass on. If they are a great pair who produce great pets in great health, you can consider holding this bird back for breeding, putting him in a giant flight with a mate to live out his days happy and free of your attempts to love him. Now, I am NOT SAYING that any untrainable bird you have should just be added to your breeding program of course, that is irresponsible. But if this behavior is due to improper socialization with humans, but the bird knows how to interact with other birds, and if his bloodline is producing quality pets, it is a possibility. You might want to start looking for a hand feeder to assist you in your time of need; I'm so sorry to hear about the hard things your family is dealing with, best of luck to you all.