I am so sorry for your situation and what is put before you.

You have been given some very good ideas. I will just spit out a couple ideas that come to me now.

Your bully is hitting maturity. This will not get better before it gets worse. She has been allowed to lead and now you are going to have to take that away if you choose to keep her. Even with the most constructed, consistent non confrontational means she is going to have to change her paradigm and this is going to stress her more.

Running around is not the same as structured exercise. She needs one on one time with running, treadmill, training or something that takes her out of her self constructed routine. She needs to be tired out. She needs to be doing what you want her to do. That would be the beginning of her groundwork.

Her anxiety is likely rooted in poor leadership. Though the fact that she left her litter at 5 weeks was a huge mistake also.IMO.

The socialization and training should have continued throughout the past 22 months. She does not have the stability and strength of temperament to do what her genetics are telling her in taking leadership. She needs total confidence in YOUR ability to be pack leader and she obviously doesn't.

Killing the other dog could just as likely be related to a prey drive or pack issue as anything to do with 'aggression'. The older dog could have acted injured, cried out, staggered....something that triggered a prey instinct. While to me it is evidence of her lack of training and control I wouldn't necessarily relate it to your being growled at or "nipped" at by her. Though all are part of her maturing.

Personally to me the fact that there are children in the household there would be no hesitation in removing her from my home right now. IF (big if) you can find a highly qualified rescue you may be able to send her there. I would not keep her in my home another day unless she is TOTALLY contained...crate, kennel, leads and two adult humans. My child is far too important to risk with a dog in this instance.

This has been brought up a couple times so I just wanted to chime in with a thought. There is a reason shelters do not adopt out dogs with a bite/killing history even with mitigating circumstances. It has nothing to do with adopt-ability, adaptability, or even causality and everything to do with liability. Because of that I will suggest to you that if this problem is not fixed in your home and you can't find a sanctuary that you should not rehome this dog to anyone even with full disclosure. It's a lawsuit waiting to happen if something/anything happens down the line even with mitigating circumstances.