Constructing fences and raised beds is a costly option if it turns out that the butterfly bush's problems are not related to weedkiller. I can totally sympathize with the situation, though, many years ago I lived in a house with a neighbor next door who hated trees. About three or four feet in from the property line I planted a grafted weeping cotoneaster. It would not have increased in height but he must have not realized that, because one day I realized it was dying. I checked around it looking for causes and found what appeared to be used motor oil poured around the trunk. It sure wasn't me, so putting two and two together!
Anyway, here's a suggestion. In your first image at the top of the thread showing what you would like, there is cleome growing in front of a fence. If you plant cleome tightly enough it forms a barrier, both visual and physical (it's a little thorny). It smells a bit too, just a heads up if that might upset the neighbor and cause more problems. If that's a concern you could try cosmos instead.
So what I'm suggesting is that if you make a long flower bed on your side of the line and plant it thickly with cleome (they're annual so you can buy started ones or start yourself from seed), you'll have your flowers in front of a fence (hers) with less cost. If she damages them with weedkiller you haven't gone to great expense and know then for sure that you'll have to try something else. Here's an illustration of what I mean, this is cleome (the old-fashioned kind, not the newer shorter "Sparkler" types) that completely disguises the wall behind. The fountain grass sticking up behind is actually planted on top of the retaining wall.
Just a thought. l too wondered about a wire fence, but on reflection thought of two problems with that. Firstly it won't stop herbicide drift, and secondly the grass will grow into the base of it and weave through it, and she'll be even more tempted to use weedkiller right up to your line to get rid of it.
Edited to add another picture of cleome (these are the shorter "Sparkler" series) used as a "hedge" to disguise a wall behind it (obviously lower than the wall in the first one above). This picture taken in fall when the plants were getting a little "tired".
