having moved a great deal over the years, I always think that the things that you either dont own, or have no control over, yet have a big influence on your new life are 1. the view 2. the neighbours and 3. the public transport around you.
You dont own the view and so I always check up on things like possible new buildings being able to be built nearby, the public transport you can check on as it is now, but I try to think how I would be affected if x no longer worked. But the big stumbling block is definitely the neighbours. You have no knowledge or say in who moves in, or when, Peoples lives change and even the really pleasant neighbour can change if their lives change.
I have no answers , just take what precautions I can. So my usual ,taking local papers, checking in things like gardeners clubs before I move. They can often tell you quite a lot about the type of soil and what they do locally, and may also know the area you are looking at, or have lived in that area before, so can often give good advice.
My personal thing that to some people might seem over the top, is I go to the area, and to the specific road if I am interested in a particular house. Take my drawn out sheet showing times and types of vehicles, and sit at the end for a day, and have my coffee and sandwiches etc with me. It has always paid dividends, good and bad, to see how the street works over a day and has alerted me to different things.
Once I have bought somewhere, I think it is very worthwhile taking photos of the garden from all angles. If unfortunately you land up with the neighbour from hell, you have clear proof of what is yours and how it looked when you arrived, so any disagreement re boundaries is squashed before they begin. It is also very nice for you, as over the years as you change your garden, you may open it for charity at some point in the future and then it is good to show how it was at the beginning. Also helps you to see where the sun is at various times of day.
With regard to this particular person, I am sorry that you have had her inflicted upon you. Her behaviour indicates that she is going to be a troublemaker whatever you do. That being so, I would be looking out pictures to show how it was before she wrecked your tree, making a copy of your land boundaries, for any future hassle from her. Then the choice seems to be either go to the solicitor to send her a letter warning her about any further incursions she might think of, or alternatively "bringing up the drawbridge" so just dealing with your own garden, having it how you like and ignoring her. She will obviously always find something to want or to complain about. Looking straight through her and not having any conversation with her, would seem less stressful to me. She will moan about whatever you do and seems to have the idea that buying a property gives her some sort of right over other people.
I hope that GN's will give you a chance to vent your feelings over time and know that we are all on your side. Oh one more thing, concentrate on the borders that do not face her so that you can sit out with your back to her side and enjoy the rest of your garden in peace. If you are working near her side, suggest you wear headphones!! (you dont have to have anything playing on them!) For now I think look around for some work to do with loppers or secateurs, It can be very satisfying as you snip, and no one can tell what you are thinking !!