What about putting up a net fence on your line and let your flowers lean against it? It could give the illusion of being against her fence, but still have the support of the net fence that is mostly invisible? Of course, it could still be a problem if she is using roundup and there is drift, but then I would gently mention to her that you would appreciate if she would spray carefully, and never on a windy day to prevent drift. If you start off sweet and she refuses, she will look the fool. But don't just NOT say anything because then she has control over you and your flowers.
If none of this seems possible you may have to resign yourself to putting up your own fence. See how much she enjoys mowing that little strip then! And she won't have to worry about your grass clippings!
