What an unfortunate situation, for you and your children as well as the person upstairs.
I find that in dealing with negative individuals, the solution has been to be as "translucent" and "transparent" as possible. Meaning, their hate/anger/emotions/actions move through you as if you are made from gossamer. It enters you, you feel and acknowledge it, but then it phases out of your body and mind and you let it go. You will need to steel yourself psionically, with a clairified Intention and lots of gentle deep breathing.
My own visualisation for times like this is a special feather suspended in air. It is light but stationary, it will move only when you want it to move, otherwise it is Stillness personified, its fibres waft in rhythm with your breathing. Practice this a few times on your own, some items that you find both powerful and grounding might help in the initial phases of getting to recognise this transparency and stillness.
The first inner shift you might experience is acceptance of their current state, why they are the way they are. And second shift, over time, you will notice there will be a lighter and less stress-filled connection you will have with her - be it meeting in person, or by having to think about her. it is almost like you have been freed from their reign of negativity - it is there, but yet it does not affect you anymore.
Lastly, there will be a shift in your view of her. You will be able to see through and beyond her anger and aggression, and instead of reacting out of fear or disdain, you will feel her underlying sorrow and pain, and maybe even spot some tell-tale signs that point towards her pain. These will help you to feel love and sympathy for her.
Eventually, even she will be able to sense a difference in YOUR energy. You will be calmer, open, less affected and completely translucent. In my own experience, suddenly the person himself will lose his aggression, (as there is nothing for it to fight or control), and become confused for a while, before settling into a gentler state of mind.
This might be something she can only experience with you. The reality is that her aggression has only reaped more aggression from other people so sadly, it has likely become a vicious cycle. Let her see and learn that with you, she does not have to be like that. Slowly and maybe for the first time in a very long time!, it will remind her of her own peaceful gentle state, and acknowledge that as being separate from her aggressive/negative side. Hopefully, that can help to bridge her conscious self and her shadow aspect, and shed light into her own behaviour/emotions.
I believe, this will help to neutralise your life, shared spaces and interactions with her. And the added benefit is that, you might be helping this individual too, long after many others have given up on her. To live with pain is in its own way, a kind of torture in itself. If you can help free her, imagine how much Light it will bring into your shared spaces.
And if you are successful at this, it will be a beautiful gift for your children as well, as it will teach them that those who are in pain are not dangerous, and that Love is the best magick of them all.
I pray for nothing but the best for you, your children and that person upstairs. May all the hurt be turned into healing. You can do it - From one soul to another, I believe in you.