Ok so I haven't RTFT but here's my opinion (ie blatantly place marking..)
The tree is fugly - conifers always are. And it will keep growing, and growing, and growing - as conifers always do. So if it's not dealt with now, it will be a bigger problem waiting to happen.
So if it's your boundary, get a shiny new fence put all the way along, as high as legally allowed (2 metres generally). If any of your neighbour's trees/hedges are in the way and encroach the boundary, you have every right to remove them as long as you give your neighbour their property back at the end (ie sling the half a tree over her side).
If it's your neighbour's boundary, get a shiny new fence put all the way along as high as legally allowed. If any of your neighbour's trees/hedges are on your side of the boundary remove them as before.
I would not negotiate with this mad woman. The law is the law is the law..... Cut her dead and document/photograph everything.
Yes half a tree will look a bit shit, but you won't be able to see it behind your 2 metre fence. And actually it will look ok from her side too - kind of. Not your problem though.