So, you think that the reason she is so timid has to do with having another very dominant baby in the clutch? I have wondered if the timidity is more a product of environment or is it innate. I am a very shy, timid person, and it feels like it is almost 100% innate, just built into my personality.
There is no telling without knowing her history. She may never have been handled and or taught to step up as a young bird. Shy birds generally don't get picked first. Most people want a bird that is sweet, loves to be held from the get go. And honestly I think too many people have high expectations on birds as companion pets and end up in the end dumping them when they don't get exactly what they want and even those tame sweet birds mature and start to bite. I do greatly appreciate that you have reached out for help from other people and you know that we do feel your sorrow and support you for all your efforts. I hope you can stay with it. I do think there will be a turning point. When my clutch of crimson babies hatched, two weeks later the father suddenly got very ill and while I was doing food cups he vomited in front of me. I immediately took him to the vet. He had lost weight and we struggled for two weeks with medicines and feeding but he eventually passed away from his illness. I hadn't anticipated pulling the babies to hand feed too soon but with one parent I made that choice. My breeding pair was not tame. I had them for three years before they laid this clutch. After the male died I would open the door up and let the female out and she would eventually fly to me for company and sit on my shoulder. I wouldn't look at her just in case she would bite my face. She was comfortable sitting on me and would gently nibble my ear lobes. I tell you all this because even a wild bird can adjust to a human for company and I certainly hope this will be the case for you. One never knows until time passes as to what it could come to be.
No, she can't fly and this is good! If she could fly I would never have been able to get her back into her cage the first couple of times that she came out, and she likely would have flown into a window.
Do you have perches on the outside of the cage? If not I would suggest putting a rope perch in a U shape over the outside of the door opening to see if she will spend some time out of the cage. Has she ever attempted to fly and landed on the floor? If she ever does I would approach her and see if she will climb onto your hand.. be patient and slow. Sit in a chair and place her on your lap to see if she can relax and visit with you and of course have a treat to reward her. If this happens and she climbs up to your shoulder sit for a few minutes to see how she reacts to being on you. If she is too uncomfortable return her to the cage on the outside perch. Instead of using your hand to remove her from your shoulder just lean over to that perch and let her climb off at her pace. She will learn to trust you because you didn't keep her from her comfort zone.
Yes, she will come out when I feed her seeds, but then quickly retreats afterward and at the slightest perception of a threat.
But she doesn't actually climb onto your hand for the treat? If she ever does, slowly turn around so she doesn't see her cage and has more focus on you. Just for a couple of minutes though. It's all about building tolerance on her part and still giving her the option of returning to her comfort zone. This is exactly how I worked with Miss Scarlette. I don't just open her door to let her out all the time... I also reach in and have her step onto my hand... ask for my kiss on the nose and then let her go to her perch. But, I can also walk away from her cage and turn my body from it to get one on one focus. I keep it short because I do know what she wants and that is to be with Casey when I let him out. We both give and take with respect.
I have tried offering her chop and lots of fresh fruits and vegetables, but she won't go near them. Her diet has now become: Avi-cakes, Nutri-Berries, safflower and sunflower seeds, and small amounts of apple.
I played them while I was away. 
Scotty still doesn't like to be held, but hams it up and dances for the vet tech with the high-pitched voice. 
He was flirts so hard it reminds me of our shameless Pistachio. She says, "Birds and dogs love me; cats hate me!" 
