What ever you do don't just "let them work it out" The umbrella cockatoo could not only serious injury the Amazon, but can kill the Amazon easily. Not sure if your Cockatoo's are mated and a pair? Likely it is hormonal behavior and the males do tend to defend the female, or he jealous? But a pair especially sure never be allow by other birds when introducing them during mating season which currently for too's it is. Plus even if they did get along before they sure always be supervised. Even if let say they were not a pair it take time for a bird to adapt and bond to each other and accept the other into the flock. You don't ever throw birds together and expect them to get along, or just let them work it out. Keep them in separate cages as well for sleep. One way to tell if you have a mated pair of cockatoo's is you see one climb the back of the other every so often to mate and they usually stay close by each other. Plus male will at times put head down and click to call over and bond with the female. Usually how you can tell which one the male and with Umbrella's female has red, or lighter brown eyes and the male usually tend to be black, or very dark brown. DNA testing is true way to tell gender.
With smaller bird it is different, but also you have to be careful. These large birds can easily injure and kill each other and a whole another story. I seen even experience breeders lose birds as one became to aggressive. With a mated pair definitely NO and a whole another complex topic.
Yes it possible to get a pair to get along with your flock, but take time and male tend to be harder to accept a new member in flock. I know I currently have a mated pair of U2's and my male use to chase Frankie my other cockatoo around when I first brought Frankie home and could only let them out separately. It took them months before my male U2 Cooper finally accepted him into flock and they get along fine now. Some birds that may never happen and you always have to keep separate.
